id	sid	tid	token	lemma	pos
ejpam-5711	1	1	european	european	PROPN
ejpam-5711	1	2	journal	journal	PROPN
ejpam-5711	1	3	of	of	ADP
ejpam-5711	1	4	pure	pure	ADJ
ejpam-5711	1	5	and	and	CCONJ
ejpam-5711	1	6	applied	applied	ADJ
ejpam-5711	1	7	mathematics	mathematic	NOUN
ejpam-5711	1	8	2025	2025	NUM
ejpam-5711	1	9	,	,	PUNCT
ejpam-5711	1	10	vol	vol	NOUN
ejpam-5711	1	11	.	.	PROPN
ejpam-5711	1	12	18	18	NUM
ejpam-5711	1	13	,	,	PUNCT
ejpam-5711	1	14	issue	issue	NOUN
ejpam-5711	1	15	1	1	NUM
ejpam-5711	1	16	,	,	PUNCT
ejpam-5711	1	17	article	article	NOUN
ejpam-5711	1	18	number	number	NOUN
ejpam-5711	1	19	5711	5711	NUM
ejpam-5711	1	20	issn	issn	PROPN
ejpam-5711	1	21	1307	1307	NUM
ejpam-5711	1	22	-	-	SYM
ejpam-5711	1	23	5543	5543	NUM
ejpam-5711	1	24	–	–	PUNCT
ejpam-5711	1	25	ejpam.com	ejpam.com	X
ejpam-5711	1	26	published	publish	VERB
ejpam-5711	1	27	by	by	ADP
ejpam-5711	1	28	new	new	PROPN
ejpam-5711	1	29	york	york	PROPN
ejpam-5711	1	30	business	business	PROPN
ejpam-5711	1	31	global	global	PROPN
ejpam-5711	1	32	m	m	PROPN
ejpam-5711	1	33	-	-	ADJ
ejpam-5711	1	34	polynomial	polynomial	ADJ
ejpam-5711	1	35	and	and	CCONJ
ejpam-5711	1	36	degree	degree	NOUN
ejpam-5711	1	37	-	-	PUNCT
ejpam-5711	1	38	based	base	VERB
ejpam-5711	1	39	topological	topological	ADJ
ejpam-5711	1	40	indices	index	NOUN
ejpam-5711	1	41	for	for	ADP
ejpam-5711	1	42	iterative	iterative	NOUN
ejpam-5711	1	43	graphs	graph	NOUN
ejpam-5711	1	44	nihad	nihad	ADJ
ejpam-5711	1	45	titan	titan	NOUN
ejpam-5711	1	46	sarhan1	sarhan1	PROPN
ejpam-5711	1	47	,	,	PUNCT
ejpam-5711	1	48	didar	didar	NOUN
ejpam-5711	1	49	abdulkhaleq	abdulkhaleq	PROPN
ejpam-5711	1	50	ali2,∗	ali2,∗	PROPN
ejpam-5711	1	51	,	,	PUNCT
ejpam-5711	1	52	gohdar	gohdar	NOUN
ejpam-5711	1	53	hashem	hashem	NOUN
ejpam-5711	1	54	mohiaddin3	mohiaddin3	NOUN
ejpam-5711	1	55	1	1	NUM
ejpam-5711	1	56	department	department	NOUN
ejpam-5711	1	57	of	of	ADP
ejpam-5711	1	58	mathematics	mathematic	NOUN
ejpam-5711	1	59	,	,	PUNCT
ejpam-5711	1	60	college	college	NOUN
ejpam-5711	1	61	of	of	ADP
ejpam-5711	1	62	education	education	NOUN
ejpam-5711	1	63	,	,	PUNCT
ejpam-5711	1	64	akre	akre	ADJ
ejpam-5711	1	65	university	university	PROPN
ejpam-5711	1	66	for	for	ADP
ejpam-5711	1	67	applied	apply	VERB
ejpam-5711	1	68	sciences	science	NOUN
ejpam-5711	1	69	,	,	PUNCT
ejpam-5711	1	70	akre	akre	PROPN
ejpam-5711	1	71	,	,	PUNCT
ejpam-5711	1	72	iraq	iraq	PROPN
ejpam-5711	1	73	2	2	NUM
ejpam-5711	1	74	department	department	NOUN
ejpam-5711	1	75	of	of	ADP
ejpam-5711	1	76	mathematics	mathematic	NOUN
ejpam-5711	1	77	,	,	PUNCT
ejpam-5711	1	78	college	college	NOUN
ejpam-5711	1	79	of	of	ADP
ejpam-5711	1	80	science	science	NOUN
ejpam-5711	1	81	,	,	PUNCT
ejpam-5711	1	82	university	university	NOUN
ejpam-5711	1	83	of	of	ADP
ejpam-5711	1	84	zakho	zakho	PROPN
ejpam-5711	1	85	,	,	PUNCT
ejpam-5711	1	86	zakho	zakho	PROPN
ejpam-5711	1	87	,	,	PUNCT
ejpam-5711	1	88	iraq	iraq	PROPN
ejpam-5711	1	89	3	3	NUM
ejpam-5711	1	90	department	department	NOUN
ejpam-5711	1	91	of	of	ADP
ejpam-5711	1	92	mathematics	mathematics	PROPN
ejpam-5711	1	93	,	,	PUNCT
ejpam-5711	1	94	college	college	NOUN
ejpam-5711	1	95	of	of	ADP
ejpam-5711	1	96	education	education	NOUN
ejpam-5711	1	97	,	,	PUNCT
ejpam-5711	1	98	university	university	NOUN
ejpam-5711	1	99	of	of	ADP
ejpam-5711	1	100	zakho	zakho	PROPN
ejpam-5711	1	101	,	,	PUNCT
ejpam-5711	1	102	zakho	zakho	PROPN
ejpam-5711	1	103	,	,	PUNCT
ejpam-5711	1	104	iraq	iraq	PROPN
ejpam-5711	1	105	abstract	abstract	NOUN
ejpam-5711	1	106	.	.	PUNCT
ejpam-5711	2	1	iterative	iterative	NOUN
ejpam-5711	2	2	graph	graph	NOUN
ejpam-5711	2	3	have	have	VERB
ejpam-5711	2	4	several	several	ADJ
ejpam-5711	2	5	applications	application	NOUN
ejpam-5711	2	6	in	in	ADP
ejpam-5711	2	7	social	social	ADJ
ejpam-5711	2	8	network	network	NOUN
ejpam-5711	2	9	analysis	analysis	NOUN
ejpam-5711	2	10	,	,	PUNCT
ejpam-5711	2	11	optimization	optimization	NOUN
ejpam-5711	2	12	problems	problem	NOUN
ejpam-5711	2	13	,	,	PUNCT
ejpam-5711	2	14	machine	machine	NOUN
ejpam-5711	2	15	learning	learning	NOUN
ejpam-5711	2	16	,	,	PUNCT
ejpam-5711	2	17	and	and	CCONJ
ejpam-5711	2	18	game	game	NOUN
ejpam-5711	2	19	theory	theory	NOUN
ejpam-5711	2	20	.	.	PUNCT
ejpam-5711	3	1	such	such	ADJ
ejpam-5711	3	2	graphs	graph	NOUN
ejpam-5711	3	3	are	be	AUX
ejpam-5711	3	4	also	also	ADV
ejpam-5711	3	5	commonly	commonly	ADV
ejpam-5711	3	6	used	use	VERB
ejpam-5711	3	7	in	in	ADP
ejpam-5711	3	8	chemistry	chemistry	NOUN
ejpam-5711	3	9	,	,	PUNCT
ejpam-5711	3	10	physics	physics	NOUN
ejpam-5711	3	11	,	,	PUNCT
ejpam-5711	3	12	and	and	CCONJ
ejpam-5711	3	13	mathematics	mathematic	NOUN
ejpam-5711	3	14	.	.	PUNCT
ejpam-5711	4	1	in	in	ADP
ejpam-5711	4	2	this	this	DET
ejpam-5711	4	3	article	article	NOUN
ejpam-5711	4	4	,	,	PUNCT
ejpam-5711	4	5	we	we	PRON
ejpam-5711	4	6	derive	derive	VERB
ejpam-5711	4	7	the	the	DET
ejpam-5711	4	8	m	m	NOUN
ejpam-5711	4	9	-	-	NOUN
ejpam-5711	4	10	polynomial	polynomial	ADJ
ejpam-5711	4	11	for	for	ADP
ejpam-5711	4	12	the	the	DET
ejpam-5711	4	13	fractal	fractal	ADJ
ejpam-5711	4	14	growth	growth	NOUN
ejpam-5711	4	15	patterns	pattern	NOUN
ejpam-5711	4	16	of	of	ADP
ejpam-5711	4	17	benzene	benzene	NOUN
ejpam-5711	4	18	(	(	PUNCT
ejpam-5711	4	19	fgbn	fgbn	NOUN
ejpam-5711	4	20	,	,	PUNCT
ejpam-5711	4	21	n	n	X
ejpam-5711	4	22	≥	≥	NOUN
ejpam-5711	4	23	1	1	NUM
ejpam-5711	4	24	)	)	PUNCT
ejpam-5711	4	25	,	,	PUNCT
ejpam-5711	4	26	the	the	DET
ejpam-5711	4	27	pythagoras	pythagoras	PROPN
ejpam-5711	4	28	tree	tree	NOUN
ejpam-5711	4	29	(	(	PUNCT
ejpam-5711	4	30	ptn	ptn	PROPN
ejpam-5711	4	31	,	,	PUNCT
ejpam-5711	4	32	n	n	PRON
ejpam-5711	4	33	≥	≥	NOUN
ejpam-5711	4	34	1	1	NUM
ejpam-5711	4	35	)	)	PUNCT
ejpam-5711	4	36	,	,	PUNCT
ejpam-5711	4	37	and	and	CCONJ
ejpam-5711	4	38	the	the	DET
ejpam-5711	4	39	benzene	benzene	NOUN
ejpam-5711	4	40	dendrimer	dendrimer	NOUN
ejpam-5711	4	41	(	(	PUNCT
ejpam-5711	4	42	dbn	dbn	PROPN
ejpam-5711	4	43	,	,	PUNCT
ejpam-5711	4	44	n	n	PRON
ejpam-5711	4	45	≥	≥	NOUN
ejpam-5711	4	46	2	2	NUM
ejpam-5711	4	47	)	)	PUNCT
ejpam-5711	4	48	.	.	PUNCT
ejpam-5711	5	1	moreover	moreover	ADV
ejpam-5711	5	2	,	,	PUNCT
ejpam-5711	5	3	we	we	PRON
ejpam-5711	5	4	compute	compute	VERB
ejpam-5711	5	5	some	some	DET
ejpam-5711	5	6	degree	degree	NOUN
ejpam-5711	5	7	-	-	PUNCT
ejpam-5711	5	8	based	base	VERB
ejpam-5711	5	9	topological	topological	ADJ
ejpam-5711	5	10	indices	index	NOUN
ejpam-5711	5	11	based	base	VERB
ejpam-5711	5	12	on	on	ADP
ejpam-5711	5	13	the	the	DET
ejpam-5711	5	14	mpolynomials	mpolynomial	NOUN
ejpam-5711	5	15	,	,	PUNCT
ejpam-5711	5	16	such	such	ADJ
ejpam-5711	5	17	as	as	ADP
ejpam-5711	5	18	the	the	DET
ejpam-5711	5	19	first	first	PROPN
ejpam-5711	5	20	zagreb	zagreb	PROPN
ejpam-5711	5	21	index	index	PROPN
ejpam-5711	5	22	,	,	PUNCT
ejpam-5711	5	23	the	the	DET
ejpam-5711	5	24	second	second	ADJ
ejpam-5711	5	25	zagreb	zagreb	PROPN
ejpam-5711	5	26	index	index	PROPN
ejpam-5711	5	27	,	,	PUNCT
ejpam-5711	5	28	the	the	DET
ejpam-5711	5	29	modified	modify	VERB
ejpam-5711	5	30	second	second	ADJ
ejpam-5711	5	31	zagreb	zagreb	PROPN
ejpam-5711	5	32	index	index	PROPN
ejpam-5711	5	33	,	,	PUNCT
ejpam-5711	5	34	the	the	DET
ejpam-5711	5	35	general	general	ADJ
ejpam-5711	5	36	randić	randić	PROPN
ejpam-5711	5	37	index	index	NOUN
ejpam-5711	5	38	,	,	PUNCT
ejpam-5711	5	39	the	the	DET
ejpam-5711	5	40	harmonic	harmonic	ADJ
ejpam-5711	5	41	index	index	NOUN
ejpam-5711	5	42	,	,	PUNCT
ejpam-5711	5	43	the	the	DET
ejpam-5711	5	44	inverse	inverse	NOUN
ejpam-5711	5	45	sum	sum	NOUN
ejpam-5711	5	46	index	index	NOUN
ejpam-5711	5	47	,	,	PUNCT
ejpam-5711	5	48	and	and	CCONJ
ejpam-5711	5	49	the	the	DET
ejpam-5711	5	50	symmetric	symmetric	ADJ
ejpam-5711	5	51	division	division	NOUN
ejpam-5711	5	52	degree	degree	NOUN
ejpam-5711	5	53	index	index	NOUN
ejpam-5711	5	54	.	.	PUNCT
ejpam-5711	6	1	finally	finally	ADV
ejpam-5711	6	2	,	,	PUNCT
ejpam-5711	6	3	we	we	PRON
ejpam-5711	6	4	presented	present	VERB
ejpam-5711	6	5	our	our	PRON
ejpam-5711	6	6	work	work	NOUN
ejpam-5711	6	7	graphically	graphically	ADV
ejpam-5711	6	8	and	and	CCONJ
ejpam-5711	6	9	compared	compare	VERB
ejpam-5711	6	10	the	the	DET
ejpam-5711	6	11	sketches	sketch	NOUN
ejpam-5711	6	12	of	of	ADP
ejpam-5711	6	13	m	m	NOUN
ejpam-5711	6	14	-	-	PUNCT
ejpam-5711	6	15	polynomials	polynomial	NOUN
ejpam-5711	6	16	and	and	CCONJ
ejpam-5711	6	17	degree	degree	NOUN
ejpam-5711	6	18	-	-	PUNCT
ejpam-5711	6	19	based	base	VERB
ejpam-5711	6	20	topological	topological	ADJ
ejpam-5711	6	21	indices	index	NOUN
ejpam-5711	6	22	.	.	PUNCT
ejpam-5711	7	1	2020	2020	NUM
ejpam-5711	7	2	mathematics	mathematic	NOUN
ejpam-5711	7	3	subject	subject	NOUN
ejpam-5711	7	4	classifications	classification	NOUN
ejpam-5711	7	5	:	:	PUNCT
ejpam-5711	7	6	05c05	05c05	NOUN
ejpam-5711	7	7	,	,	PUNCT
ejpam-5711	7	8	05c07	05c07	NOUN
ejpam-5711	7	9	,	,	PUNCT
ejpam-5711	7	10	05c10	05c10	ADJ
ejpam-5711	7	11	,	,	PUNCT
ejpam-5711	7	12	94c15	94c15	NUM
ejpam-5711	7	13	key	key	ADJ
ejpam-5711	7	14	words	word	NOUN
ejpam-5711	7	15	and	and	CCONJ
ejpam-5711	7	16	phrases	phrase	NOUN
ejpam-5711	7	17	:	:	PUNCT
ejpam-5711	7	18	m	m	NOUN
ejpam-5711	7	19	-	-	ADJ
ejpam-5711	7	20	polynomial	polynomial	ADJ
ejpam-5711	7	21	,	,	PUNCT
ejpam-5711	7	22	topological	topological	ADJ
ejpam-5711	7	23	indices	index	NOUN
ejpam-5711	7	24	,	,	PUNCT
ejpam-5711	7	25	fractal	fractal	PROPN
ejpam-5711	7	26	,	,	PUNCT
ejpam-5711	7	27	pythagoras	pythagoras	PROPN
ejpam-5711	7	28	tree	tree	PROPN
ejpam-5711	7	29	,	,	PUNCT
ejpam-5711	7	30	benzene	benzene	NOUN
ejpam-5711	7	31	dendrimer	dendrimer	NOUN
ejpam-5711	7	32	1	1	NUM
ejpam-5711	7	33	.	.	PUNCT
ejpam-5711	8	1	introduction	introduction	NOUN
ejpam-5711	8	2	polynomials	polynomial	NOUN
ejpam-5711	8	3	are	be	AUX
ejpam-5711	8	4	tools	tool	NOUN
ejpam-5711	8	5	in	in	ADP
ejpam-5711	8	6	chemical	chemical	NOUN
ejpam-5711	8	7	graph	graph	NOUN
ejpam-5711	8	8	theory	theory	NOUN
ejpam-5711	8	9	used	use	VERB
ejpam-5711	8	10	to	to	PART
ejpam-5711	8	11	collect	collect	VERB
ejpam-5711	8	12	information	information	NOUN
ejpam-5711	8	13	about	about	ADP
ejpam-5711	8	14	molecular	molecular	ADJ
ejpam-5711	8	15	graphs	graph	NOUN
ejpam-5711	8	16	and	and	CCONJ
ejpam-5711	8	17	thus	thus	ADV
ejpam-5711	8	18	display	display	VERB
ejpam-5711	8	19	properties	property	NOUN
ejpam-5711	8	20	of	of	ADP
ejpam-5711	8	21	the	the	DET
ejpam-5711	8	22	molecular	molecular	ADJ
ejpam-5711	8	23	graph	graph	NOUN
ejpam-5711	8	24	without	without	ADP
ejpam-5711	8	25	using	use	VERB
ejpam-5711	8	26	quantum	quantum	ADJ
ejpam-5711	8	27	mechanics	mechanic	NOUN
ejpam-5711	8	28	.	.	PUNCT
ejpam-5711	9	1	a	a	DET
ejpam-5711	9	2	molecular	molecular	ADJ
ejpam-5711	9	3	graph	graph	NOUN
ejpam-5711	9	4	is	be	AUX
ejpam-5711	9	5	generated	generate	VERB
ejpam-5711	9	6	by	by	ADP
ejpam-5711	9	7	the	the	DET
ejpam-5711	9	8	conversion	conversion	NOUN
ejpam-5711	9	9	of	of	ADP
ejpam-5711	9	10	a	a	DET
ejpam-5711	9	11	chemical	chemical	NOUN
ejpam-5711	9	12	molecule	molecule	NOUN
ejpam-5711	9	13	into	into	ADP
ejpam-5711	9	14	a	a	DET
ejpam-5711	9	15	graph	graph	NOUN
ejpam-5711	9	16	in	in	SCONJ
ejpam-5711	9	17	which	which	DET
ejpam-5711	9	18	vertices	vertex	NOUN
ejpam-5711	9	19	and	and	CCONJ
ejpam-5711	9	20	edges	edge	NOUN
ejpam-5711	9	21	are	be	AUX
ejpam-5711	9	22	represented	represent	VERB
ejpam-5711	9	23	by	by	ADP
ejpam-5711	9	24	atoms	atom	NOUN
ejpam-5711	9	25	and	and	CCONJ
ejpam-5711	9	26	bonds	bond	NOUN
ejpam-5711	9	27	,	,	PUNCT
ejpam-5711	9	28	respectively	respectively	ADV
ejpam-5711	9	29	.	.	PUNCT
ejpam-5711	10	1	let	let	VERB
ejpam-5711	10	2	h(v	h(v	NOUN
ejpam-5711	10	3	,	,	PUNCT
ejpam-5711	10	4	e	e	NOUN
ejpam-5711	10	5	)	)	PUNCT
ejpam-5711	10	6	be	be	AUX
ejpam-5711	10	7	a	a	DET
ejpam-5711	10	8	simple	simple	ADJ
ejpam-5711	10	9	connected	connected	ADJ
ejpam-5711	10	10	undirected	undirected	ADJ
ejpam-5711	10	11	graphs	graph	NOUN
ejpam-5711	10	12	,	,	PUNCT
ejpam-5711	10	13	where	where	SCONJ
ejpam-5711	10	14	v(h	v(h	NOUN
ejpam-5711	10	15	)	)	PUNCT
ejpam-5711	10	16	denotes	denote	VERB
ejpam-5711	10	17	the	the	DET
ejpam-5711	10	18	set	set	NOUN
ejpam-5711	10	19	of	of	ADP
ejpam-5711	10	20	vertices	vertex	NOUN
ejpam-5711	10	21	and	and	CCONJ
ejpam-5711	10	22	e(h	e(h	PROPN
ejpam-5711	10	23	)	)	PUNCT
ejpam-5711	10	24	denotes	denote	VERB
ejpam-5711	10	25	the	the	DET
ejpam-5711	10	26	set	set	NOUN
ejpam-5711	10	27	of	of	ADP
ejpam-5711	10	28	edges	edge	NOUN
ejpam-5711	10	29	.	.	PUNCT
ejpam-5711	11	1	number	number	NOUN
ejpam-5711	11	2	of	of	ADP
ejpam-5711	11	3	vertices	vertex	NOUN
ejpam-5711	11	4	|v	|v	PROPN
ejpam-5711	11	5	(	(	PUNCT
ejpam-5711	11	6	h)|	h)|	PROPN
ejpam-5711	11	7	is	be	AUX
ejpam-5711	11	8	the	the	DET
ejpam-5711	11	9	order	order	NOUN
ejpam-5711	11	10	of	of	ADP
ejpam-5711	11	11	graph	graph	NOUN
ejpam-5711	11	12	and	and	CCONJ
ejpam-5711	11	13	number	number	NOUN
ejpam-5711	11	14	of	of	ADP
ejpam-5711	11	15	edges	edge	NOUN
ejpam-5711	11	16	|e(h)|	|e(h)|	PROPN
ejpam-5711	11	17	is	be	AUX
ejpam-5711	11	18	the	the	DET
ejpam-5711	11	19	size	size	NOUN
ejpam-5711	11	20	of	of	ADP
ejpam-5711	11	21	graph	graph	NOUN
ejpam-5711	11	22	.	.	PUNCT
ejpam-5711	12	1	connected	connected	ADJ
ejpam-5711	12	2	graph	graph	NOUN
ejpam-5711	12	3	is	be	AUX
ejpam-5711	12	4	a	a	DET
ejpam-5711	12	5	graph	graph	NOUN
ejpam-5711	12	6	in	in	ADP
ejpam-5711	12	7	which	which	PRON
ejpam-5711	12	8	there	there	PRON
ejpam-5711	12	9	exists	exist	VERB
ejpam-5711	12	10	a	a	DET
ejpam-5711	12	11	path	path	NOUN
ejpam-5711	12	12	between	between	ADP
ejpam-5711	12	13	every	every	DET
ejpam-5711	12	14	pair	pair	NOUN
ejpam-5711	12	15	of	of	ADP
ejpam-5711	12	16	vertices	vertex	NOUN
ejpam-5711	12	17	.	.	PUNCT
ejpam-5711	13	1	a	a	DET
ejpam-5711	13	2	vertex	vertex	NOUN
ejpam-5711	13	3	u	u	NOUN
ejpam-5711	13	4	’s	’s	NOUN
ejpam-5711	13	5	degree	degree	NOUN
ejpam-5711	13	6	,	,	PUNCT
ejpam-5711	13	7	denoted	denote	VERB
ejpam-5711	13	8	as	as	ADP
ejpam-5711	13	9	du	du	NOUN
ejpam-5711	13	10	,	,	PUNCT
ejpam-5711	13	11	refers	refer	VERB
ejpam-5711	13	12	∗corresponding	∗corresponde	VERB
ejpam-5711	13	13	author	author	NOUN
ejpam-5711	13	14	.	.	PUNCT
ejpam-5711	14	1	doi	doi	NOUN
ejpam-5711	14	2	:	:	PUNCT
ejpam-5711	14	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5711	https://doi.org/10.29020/nybg.ejpam.v18i1.5711	NOUN
ejpam-5711	14	4	email	email	NOUN
ejpam-5711	14	5	addresses	address	NOUN
ejpam-5711	14	6	:	:	PUNCT
ejpam-5711	14	7	nihad.titan@auas.edu.krd	nihad.titan@auas.edu.krd	X
ejpam-5711	14	8	(	(	PUNCT
ejpam-5711	14	9	n.	n.	NOUN
ejpam-5711	14	10	t.	t.	PROPN
ejpam-5711	14	11	sarhan	sarhan	PROPN
ejpam-5711	14	12	)	)	PUNCT
ejpam-5711	14	13	,	,	PUNCT
ejpam-5711	14	14	didar.ali@uoz.edu.krd	didar.ali@uoz.edu.krd	PROPN
ejpam-5711	14	15	(	(	PUNCT
ejpam-5711	14	16	d.	d.	PROPN
ejpam-5711	14	17	a.	a.	PROPN
ejpam-5711	14	18	ali	ali	PROPN
ejpam-5711	14	19	)	)	PUNCT
ejpam-5711	14	20	,	,	PUNCT
ejpam-5711	14	21	gohdar.mohiaddin@uoz.edu.krd	gohdar.mohiaddin@uoz.edu.krd	PROPN
ejpam-5711	14	22	(	(	PUNCT
ejpam-5711	14	23	g.	g.	PROPN
ejpam-5711	14	24	h.	h.	PROPN
ejpam-5711	14	25	mohiaddin	mohiaddin	PROPN
ejpam-5711	14	26	)	)	PUNCT
ejpam-5711	14	27	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5711	15	1	1	1	NUM
ejpam-5711	15	2	copyright	copyright	NOUN
ejpam-5711	15	3	:	:	PUNCT
ejpam-5711	15	4	©	©	PROPN
ejpam-5711	15	5	2025	2025	NUM
ejpam-5711	15	6	the	the	DET
ejpam-5711	15	7	author(s	author(s	NOUN
ejpam-5711	15	8	)	)	PUNCT
ejpam-5711	15	9	.	.	PUNCT
ejpam-5711	16	1	(	(	PUNCT
ejpam-5711	16	2	cc	cc	NOUN
ejpam-5711	16	3	by	by	ADP
ejpam-5711	16	4	-	-	PUNCT
ejpam-5711	16	5	nc	nc	PROPN
ejpam-5711	16	6	4.0	4.0	NUM
ejpam-5711	16	7	)	)	PUNCT
ejpam-5711	16	8	n.	n.	NOUN
ejpam-5711	16	9	t.	t.	PROPN
ejpam-5711	16	10	sarhan	sarhan	PROPN
ejpam-5711	16	11	,	,	PUNCT
ejpam-5711	16	12	d.	d.	PROPN
ejpam-5711	16	13	a.	a.	PROPN
ejpam-5711	16	14	ali	ali	PROPN
ejpam-5711	16	15	,	,	PUNCT
ejpam-5711	16	16	g.	g.	PROPN
ejpam-5711	16	17	h.	h.	PROPN
ejpam-5711	17	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	17	2	/	/	SYM
ejpam-5711	17	3	eur	eur	PROPN
ejpam-5711	17	4	.	.	PUNCT
ejpam-5711	18	1	j.	j.	PROPN
ejpam-5711	18	2	pure	pure	PROPN
ejpam-5711	18	3	appl	appl	PROPN
ejpam-5711	18	4	.	.	PROPN
ejpam-5711	18	5	math	math	PROPN
ejpam-5711	18	6	,	,	PUNCT
ejpam-5711	18	7	18	18	NUM
ejpam-5711	18	8	(	(	PUNCT
ejpam-5711	18	9	1	1	NUM
ejpam-5711	18	10	)	)	PUNCT
ejpam-5711	18	11	(	(	PUNCT
ejpam-5711	18	12	2025	2025	NUM
ejpam-5711	18	13	)	)	PUNCT
ejpam-5711	18	14	,	,	PUNCT
ejpam-5711	18	15	5711	5711	NUM
ejpam-5711	18	16	2	2	NUM
ejpam-5711	18	17	of	of	ADP
ejpam-5711	18	18	15	15	NUM
ejpam-5711	18	19	to	to	ADP
ejpam-5711	18	20	the	the	DET
ejpam-5711	18	21	number	number	NOUN
ejpam-5711	18	22	of	of	ADP
ejpam-5711	18	23	edges	edge	NOUN
ejpam-5711	18	24	that	that	PRON
ejpam-5711	18	25	are	be	AUX
ejpam-5711	18	26	adjacent	adjacent	ADJ
ejpam-5711	18	27	to	to	ADP
ejpam-5711	18	28	vertex	vertex	PROPN
ejpam-5711	18	29	u.	u.	PROPN
ejpam-5711	18	30	topological	topological	PROPN
ejpam-5711	18	31	indices	index	NOUN
ejpam-5711	18	32	are	be	AUX
ejpam-5711	18	33	numerical	numerical	ADJ
ejpam-5711	18	34	parameters	parameter	NOUN
ejpam-5711	18	35	associated	associate	VERB
ejpam-5711	18	36	with	with	ADP
ejpam-5711	18	37	a	a	DET
ejpam-5711	18	38	molecular	molecular	ADJ
ejpam-5711	18	39	graph	graph	NOUN
ejpam-5711	18	40	that	that	PRON
ejpam-5711	18	41	characterizes	characterize	VERB
ejpam-5711	18	42	its	its	PRON
ejpam-5711	18	43	topology	topology	NOUN
ejpam-5711	18	44	.	.	PUNCT
ejpam-5711	19	1	the	the	DET
ejpam-5711	19	2	role	role	NOUN
ejpam-5711	19	3	of	of	ADP
ejpam-5711	19	4	algebraic	algebraic	ADJ
ejpam-5711	19	5	polynomials	polynomial	NOUN
ejpam-5711	19	6	is	be	AUX
ejpam-5711	19	7	central	central	ADJ
ejpam-5711	19	8	to	to	ADP
ejpam-5711	19	9	the	the	DET
ejpam-5711	19	10	development	development	NOUN
ejpam-5711	19	11	of	of	ADP
ejpam-5711	19	12	chemical	chemical	NOUN
ejpam-5711	19	13	graph	graph	NOUN
ejpam-5711	19	14	theory	theory	NOUN
ejpam-5711	19	15	,	,	PUNCT
ejpam-5711	19	16	such	such	ADJ
ejpam-5711	19	17	as	as	ADP
ejpam-5711	19	18	the	the	DET
ejpam-5711	19	19	hosoya	hosoya	NOUN
ejpam-5711	19	20	polynomial	polynomial	NOUN
ejpam-5711	19	21	[	[	X
ejpam-5711	19	22	12	12	NUM
ejpam-5711	19	23	]	]	PUNCT
ejpam-5711	19	24	,	,	PUNCT
ejpam-5711	19	25	and	and	CCONJ
ejpam-5711	19	26	the	the	DET
ejpam-5711	19	27	acyclic	acyclic	ADJ
ejpam-5711	19	28	polynomial	polynomial	NOUN
ejpam-5711	19	29	of	of	ADP
ejpam-5711	19	30	a	a	DET
ejpam-5711	19	31	graph	graph	NOUN
ejpam-5711	19	32	[	[	X
ejpam-5711	19	33	10	10	NUM
ejpam-5711	19	34	]	]	PUNCT
ejpam-5711	19	35	.	.	PUNCT
ejpam-5711	20	1	deutsch	deutsch	NOUN
ejpam-5711	20	2	and	and	CCONJ
ejpam-5711	20	3	klavžar	klavžar	PROPN
ejpam-5711	20	4	[	[	X
ejpam-5711	20	5	6	6	NUM
ejpam-5711	20	6	]	]	PUNCT
ejpam-5711	20	7	,	,	PUNCT
ejpam-5711	20	8	introduced	introduce	VERB
ejpam-5711	20	9	the	the	DET
ejpam-5711	20	10	m	m	NOUN
ejpam-5711	20	11	-	-	NOUN
ejpam-5711	20	12	polynomial	polynomial	ADJ
ejpam-5711	20	13	with	with	ADP
ejpam-5711	20	14	the	the	DET
ejpam-5711	20	15	aim	aim	NOUN
ejpam-5711	20	16	of	of	ADP
ejpam-5711	20	17	achieving	achieve	VERB
ejpam-5711	20	18	similar	similar	ADJ
ejpam-5711	20	19	goals	goal	NOUN
ejpam-5711	20	20	as	as	ADP
ejpam-5711	20	21	the	the	DET
ejpam-5711	20	22	hosoya	hosoya	NOUN
ejpam-5711	20	23	polynomial	polynomial	ADJ
ejpam-5711	20	24	,	,	PUNCT
ejpam-5711	20	25	specifically	specifically	ADV
ejpam-5711	20	26	in	in	ADP
ejpam-5711	20	27	deriving	derive	VERB
ejpam-5711	20	28	closed	closed	ADJ
ejpam-5711	20	29	-	-	PUNCT
ejpam-5711	20	30	form	form	NOUN
ejpam-5711	20	31	expressions	expression	NOUN
ejpam-5711	20	32	for	for	ADP
ejpam-5711	20	33	numerous	numerous	ADJ
ejpam-5711	20	34	degree	degree	NOUN
ejpam-5711	20	35	-	-	PUNCT
ejpam-5711	20	36	based	base	VERB
ejpam-5711	20	37	topological	topological	ADJ
ejpam-5711	20	38	indices	index	NOUN
ejpam-5711	20	39	.	.	PUNCT
ejpam-5711	21	1	several	several	ADJ
ejpam-5711	21	2	researchers	researcher	NOUN
ejpam-5711	21	3	have	have	AUX
ejpam-5711	21	4	calculated	calculate	VERB
ejpam-5711	21	5	the	the	DET
ejpam-5711	21	6	mpolynomial	mpolynomial	ADJ
ejpam-5711	21	7	and	and	CCONJ
ejpam-5711	21	8	associated	associated	ADJ
ejpam-5711	21	9	topological	topological	ADJ
ejpam-5711	21	10	indices	index	NOUN
ejpam-5711	21	11	for	for	ADP
ejpam-5711	21	12	well	well	ADV
ejpam-5711	21	13	-	-	PUNCT
ejpam-5711	21	14	known	know	VERB
ejpam-5711	21	15	graphs.examples	graphs.example	NOUN
ejpam-5711	21	16	include	include	VERB
ejpam-5711	21	17	the	the	DET
ejpam-5711	21	18	m	m	NOUN
ejpam-5711	21	19	-	-	ADJ
ejpam-5711	21	20	polynomial	polynomial	ADJ
ejpam-5711	21	21	and	and	CCONJ
ejpam-5711	21	22	topological	topological	ADJ
ejpam-5711	21	23	indices	index	NOUN
ejpam-5711	21	24	of	of	ADP
ejpam-5711	21	25	nanostar	nanostar	ADJ
ejpam-5711	21	26	dendrimers	dendrimer	NOUN
ejpam-5711	21	27	and	and	CCONJ
ejpam-5711	21	28	polyhex	polyhex	NOUN
ejpam-5711	21	29	nanotubes	nanotube	NOUN
ejpam-5711	21	30	[	[	X
ejpam-5711	21	31	17	17	NUM
ejpam-5711	21	32	,	,	PUNCT
ejpam-5711	21	33	18	18	NUM
ejpam-5711	21	34	]	]	PUNCT
ejpam-5711	21	35	,	,	PUNCT
ejpam-5711	21	36	linear	linear	ADJ
ejpam-5711	21	37	chains	chain	NOUN
ejpam-5711	21	38	of	of	ADP
ejpam-5711	21	39	benzene	benzene	NOUN
ejpam-5711	21	40	,	,	PUNCT
ejpam-5711	21	41	naphthalene	naphthalene	NOUN
ejpam-5711	21	42	,	,	PUNCT
ejpam-5711	21	43	and	and	CCONJ
ejpam-5711	21	44	anthracene	anthracene	VERB
ejpam-5711	21	45	[	[	X
ejpam-5711	21	46	14	14	NUM
ejpam-5711	21	47	]	]	X
ejpam-5711	21	48	,	,	PUNCT
ejpam-5711	21	49	benzene	benzene	NOUN
ejpam-5711	21	50	rings	ring	NOUN
ejpam-5711	21	51	embedded	embed	VERB
ejpam-5711	21	52	in	in	ADP
ejpam-5711	21	53	p	p	NOUN
ejpam-5711	21	54	-	-	PUNCT
ejpam-5711	21	55	type	type	NOUN
ejpam-5711	21	56	surface	surface	NOUN
ejpam-5711	21	57	networks	network	NOUN
ejpam-5711	21	58	,	,	PUNCT
ejpam-5711	21	59	zigzag	zigzag	NOUN
ejpam-5711	21	60	and	and	CCONJ
ejpam-5711	21	61	rhombic	rhombic	ADJ
ejpam-5711	21	62	benzenoid	benzenoid	NOUN
ejpam-5711	21	63	systems	system	NOUN
ejpam-5711	22	1	[	[	X
ejpam-5711	22	2	1	1	NUM
ejpam-5711	22	3	]	]	PUNCT
ejpam-5711	22	4	,	,	PUNCT
ejpam-5711	22	5	generalized	generalize	VERB
ejpam-5711	22	6	sierpinski	sierpinski	ADJ
ejpam-5711	22	7	networks	network	NOUN
ejpam-5711	22	8	[	[	X
ejpam-5711	22	9	8	8	NUM
ejpam-5711	22	10	]	]	PUNCT
ejpam-5711	22	11	,	,	PUNCT
ejpam-5711	22	12	hourglass	hourglass	NOUN
ejpam-5711	22	13	,	,	PUNCT
ejpam-5711	22	14	triangular	triangular	NOUN
ejpam-5711	22	15	,	,	PUNCT
ejpam-5711	22	16	as	as	ADV
ejpam-5711	22	17	well	well	ADV
ejpam-5711	22	18	as	as	ADP
ejpam-5711	22	19	jagged	jagged	ADJ
ejpam-5711	22	20	-	-	PUNCT
ejpam-5711	22	21	rectangle	rectangle	NOUN
ejpam-5711	22	22	benzenoid	benzenoid	NOUN
ejpam-5711	22	23	systems	system	NOUN
ejpam-5711	22	24	detailed	detail	VERB
ejpam-5711	22	25	[	[	X
ejpam-5711	22	26	13	13	NUM
ejpam-5711	22	27	]	]	PUNCT
ejpam-5711	22	28	,	,	PUNCT
ejpam-5711	22	29	generalized	generalized	ADJ
ejpam-5711	22	30	zegrab	zegrab	NOUN
ejpam-5711	22	31	index	index	NOUN
ejpam-5711	22	32	,	,	PUNCT
ejpam-5711	22	33	fourth	fourth	ADJ
ejpam-5711	22	34	version	version	NOUN
ejpam-5711	22	35	of	of	ADP
ejpam-5711	22	36	atom	atom	NOUN
ejpam-5711	22	37	-	-	PUNCT
ejpam-5711	22	38	bond	bond	NOUN
ejpam-5711	22	39	connectivity	connectivity	NOUN
ejpam-5711	22	40	and	and	CCONJ
ejpam-5711	22	41	fifth	fifth	ADJ
ejpam-5711	22	42	version	version	NOUN
ejpam-5711	22	43	of	of	ADP
ejpam-5711	22	44	geometric	geometric	ADJ
ejpam-5711	22	45	-	-	PUNCT
ejpam-5711	22	46	arithmetic	arithmetic	ADJ
ejpam-5711	22	47	index	index	NOUN
ejpam-5711	22	48	for	for	ADP
ejpam-5711	22	49	an	an	DET
ejpam-5711	22	50	infinite	infinite	ADJ
ejpam-5711	22	51	class	class	NOUN
ejpam-5711	22	52	of	of	ADP
ejpam-5711	22	53	titania	titania	NOUN
ejpam-5711	22	54	nanotubes	nanotube	NOUN
ejpam-5711	22	55	tio−2[m	tio−2[m	PROPN
ejpam-5711	22	56	,	,	PUNCT
ejpam-5711	22	57	n	n	CCONJ
ejpam-5711	22	58	]	]	X
ejpam-5711	23	1	[	[	X
ejpam-5711	23	2	15	15	NUM
ejpam-5711	23	3	]	]	PUNCT
ejpam-5711	23	4	,	,	PUNCT
ejpam-5711	23	5	computation	computation	NOUN
ejpam-5711	23	6	of	of	ADP
ejpam-5711	23	7	benzenoid	benzenoid	NOUN
ejpam-5711	23	8	planar	planar	ADJ
ejpam-5711	23	9	octahedron	octahedron	NOUN
ejpam-5711	23	10	networks	network	NOUN
ejpam-5711	23	11	by	by	ADP
ejpam-5711	23	12	using	use	VERB
ejpam-5711	23	13	topological	topological	ADJ
ejpam-5711	23	14	indices	index	NOUN
ejpam-5711	23	15	[	[	X
ejpam-5711	23	16	2	2	NUM
ejpam-5711	23	17	]	]	PUNCT
ejpam-5711	23	18	,	,	PUNCT
ejpam-5711	23	19	and	and	CCONJ
ejpam-5711	23	20	topological	topological	ADJ
ejpam-5711	23	21	indices	index	NOUN
ejpam-5711	23	22	of	of	ADP
ejpam-5711	23	23	third	third	ADJ
ejpam-5711	23	24	types	type	NOUN
ejpam-5711	23	25	of	of	ADP
ejpam-5711	23	26	hex	hex	NOUN
ejpam-5711	23	27	-	-	PUNCT
ejpam-5711	23	28	derived	derive	VERB
ejpam-5711	23	29	networks	network	NOUN
ejpam-5711	23	30	[	[	X
ejpam-5711	23	31	3	3	NUM
ejpam-5711	23	32	]	]	PUNCT
ejpam-5711	23	33	.	.	PUNCT
ejpam-5711	24	1	in	in	ADP
ejpam-5711	24	2	this	this	DET
ejpam-5711	24	3	paper	paper	NOUN
ejpam-5711	24	4	,	,	PUNCT
ejpam-5711	24	5	we	we	PRON
ejpam-5711	24	6	derive	derive	VERB
ejpam-5711	24	7	the	the	DET
ejpam-5711	24	8	m	m	NOUN
ejpam-5711	24	9	-	-	NOUN
ejpam-5711	24	10	polynomial	polynomial	ADJ
ejpam-5711	24	11	for	for	ADP
ejpam-5711	24	12	the	the	DET
ejpam-5711	24	13	fractal	fractal	ADJ
ejpam-5711	24	14	growth	growth	NOUN
ejpam-5711	24	15	patterns	pattern	NOUN
ejpam-5711	24	16	of	of	ADP
ejpam-5711	24	17	benzene	benzene	NOUN
ejpam-5711	24	18	(	(	PUNCT
ejpam-5711	24	19	fgbn	fgbn	NOUN
ejpam-5711	24	20	,	,	PUNCT
ejpam-5711	24	21	n	n	X
ejpam-5711	24	22	≥	≥	NOUN
ejpam-5711	24	23	1	1	NUM
ejpam-5711	24	24	)	)	PUNCT
ejpam-5711	24	25	,	,	PUNCT
ejpam-5711	24	26	the	the	DET
ejpam-5711	24	27	pythagoras	pythagoras	PROPN
ejpam-5711	24	28	tree	tree	NOUN
ejpam-5711	24	29	(	(	PUNCT
ejpam-5711	24	30	ptn	ptn	PROPN
ejpam-5711	24	31	,	,	PUNCT
ejpam-5711	24	32	n	n	PRON
ejpam-5711	24	33	≥	≥	NOUN
ejpam-5711	24	34	1	1	NUM
ejpam-5711	24	35	)	)	PUNCT
ejpam-5711	24	36	,	,	PUNCT
ejpam-5711	24	37	and	and	CCONJ
ejpam-5711	24	38	the	the	DET
ejpam-5711	24	39	benzene	benzene	NOUN
ejpam-5711	24	40	dendrimer	dendrimer	NOUN
ejpam-5711	24	41	(	(	PUNCT
ejpam-5711	24	42	dbn	dbn	PROPN
ejpam-5711	24	43	,	,	PUNCT
ejpam-5711	24	44	n	n	PRON
ejpam-5711	24	45	≥	≥	NOUN
ejpam-5711	24	46	2	2	NUM
ejpam-5711	24	47	)	)	PUNCT
ejpam-5711	24	48	.	.	PUNCT
ejpam-5711	25	1	moreover	moreover	ADV
ejpam-5711	25	2	,	,	PUNCT
ejpam-5711	25	3	we	we	PRON
ejpam-5711	25	4	compute	compute	VERB
ejpam-5711	25	5	some	some	DET
ejpam-5711	25	6	degree	degree	NOUN
ejpam-5711	25	7	-	-	PUNCT
ejpam-5711	25	8	based	base	VERB
ejpam-5711	25	9	topological	topological	ADJ
ejpam-5711	25	10	indices	index	NOUN
ejpam-5711	25	11	based	base	VERB
ejpam-5711	25	12	on	on	ADP
ejpam-5711	25	13	the	the	DET
ejpam-5711	25	14	m	m	NOUN
ejpam-5711	25	15	-	-	NOUN
ejpam-5711	25	16	polynomials	polynomial	NOUN
ejpam-5711	25	17	.	.	PUNCT
ejpam-5711	26	1	definition	definition	NOUN
ejpam-5711	26	2	1	1	NUM
ejpam-5711	26	3	.	.	PUNCT
ejpam-5711	27	1	[	[	X
ejpam-5711	27	2	6	6	NUM
ejpam-5711	27	3	]	]	PUNCT
ejpam-5711	27	4	let	let	VERB
ejpam-5711	27	5	h	h	PRON
ejpam-5711	27	6	be	be	AUX
ejpam-5711	27	7	a	a	DET
ejpam-5711	27	8	graph	graph	NOUN
ejpam-5711	27	9	and	and	CCONJ
ejpam-5711	27	10	mα	mα	NOUN
ejpam-5711	27	11	,	,	PUNCT
ejpam-5711	27	12	β	β	X
ejpam-5711	27	13	be	be	VERB
ejpam-5711	27	14	the	the	DET
ejpam-5711	27	15	count	count	NOUN
ejpam-5711	27	16	of	of	ADP
ejpam-5711	27	17	edges	edge	NOUN
ejpam-5711	27	18	e	e	NOUN
ejpam-5711	27	19	=	=	PUNCT
ejpam-5711	27	20	uv	uv	PROPN
ejpam-5711	27	21	∈	∈	PROPN
ejpam-5711	27	22	e(h	e(h	PROPN
ejpam-5711	27	23	)	)	PUNCT
ejpam-5711	27	24	such	such	ADJ
ejpam-5711	27	25	that	that	SCONJ
ejpam-5711	27	26	(	(	PUNCT
ejpam-5711	27	27	du	du	PROPN
ejpam-5711	27	28	,	,	PUNCT
ejpam-5711	27	29	dv	dv	PROPN
ejpam-5711	27	30	)	)	PUNCT
ejpam-5711	27	31	=	=	SYM
ejpam-5711	27	32	(	(	PUNCT
ejpam-5711	27	33	α	α	X
ejpam-5711	27	34	,	,	PUNCT
ejpam-5711	27	35	β	β	NOUN
ejpam-5711	27	36	)	)	PUNCT
ejpam-5711	27	37	,	,	PUNCT
ejpam-5711	27	38	then	then	ADV
ejpam-5711	27	39	the	the	DET
ejpam-5711	27	40	m	m	NOUN
ejpam-5711	27	41	-	-	ADJ
ejpam-5711	27	42	polynomial	polynomial	ADJ
ejpam-5711	27	43	of	of	ADP
ejpam-5711	27	44	h	h	NOUN
ejpam-5711	27	45	is	be	AUX
ejpam-5711	27	46	defined	define	VERB
ejpam-5711	27	47	as	as	ADP
ejpam-5711	27	48	:	:	PUNCT
ejpam-5711	27	49	m(h;x	m(h;x	PROPN
ejpam-5711	27	50	,	,	PUNCT
ejpam-5711	27	51	y	y	NOUN
ejpam-5711	27	52	)	)	PUNCT
ejpam-5711	28	1	=	=	PUNCT
ejpam-5711	28	2	∑	∑	PUNCT
ejpam-5711	28	3	δ≤α≤β≤∆	δ≤α≤β≤∆	PROPN
ejpam-5711	28	4	mα	mα	PROPN
ejpam-5711	28	5	,	,	PUNCT
ejpam-5711	28	6	βx	βx	VERB
ejpam-5711	28	7	αyβ	αyβ	NOUN
ejpam-5711	28	8	.	.	PUNCT
ejpam-5711	29	1	here	here	ADV
ejpam-5711	29	2	,	,	PUNCT
ejpam-5711	29	3	δ	δ	PROPN
ejpam-5711	29	4	denotes	denote	VERB
ejpam-5711	29	5	the	the	DET
ejpam-5711	29	6	minimum	minimum	NOUN
ejpam-5711	29	7	degree	degree	NOUN
ejpam-5711	29	8	in	in	ADP
ejpam-5711	29	9	h	h	NOUN
ejpam-5711	29	10	,	,	PUNCT
ejpam-5711	29	11	while	while	SCONJ
ejpam-5711	29	12	∆	∆	PROPN
ejpam-5711	29	13	denotes	denote	VERB
ejpam-5711	29	14	the	the	DET
ejpam-5711	29	15	maximum	maximum	ADJ
ejpam-5711	29	16	degree	degree	NOUN
ejpam-5711	29	17	in	in	ADP
ejpam-5711	29	18	h.	h.	PROPN
ejpam-5711	29	19	several	several	ADJ
ejpam-5711	29	20	indices	index	NOUN
ejpam-5711	29	21	are	be	AUX
ejpam-5711	29	22	derived	derive	VERB
ejpam-5711	29	23	from	from	ADP
ejpam-5711	29	24	polynomials	polynomial	NOUN
ejpam-5711	29	25	.	.	PUNCT
ejpam-5711	30	1	the	the	DET
ejpam-5711	30	2	first	first	ADJ
ejpam-5711	30	3	index	index	NOUN
ejpam-5711	30	4	is	be	AUX
ejpam-5711	30	5	the	the	DET
ejpam-5711	30	6	wiener	wiener	NOUN
ejpam-5711	30	7	index	index	NOUN
ejpam-5711	30	8	,	,	PUNCT
ejpam-5711	30	9	also	also	ADV
ejpam-5711	30	10	known	know	VERB
ejpam-5711	30	11	as	as	ADP
ejpam-5711	30	12	the	the	DET
ejpam-5711	30	13	path	path	NOUN
ejpam-5711	30	14	number	number	NOUN
ejpam-5711	30	15	,	,	PUNCT
ejpam-5711	30	16	introduced	introduce	VERB
ejpam-5711	30	17	by	by	ADP
ejpam-5711	30	18	wiener	wiener	NOUN
ejpam-5711	30	19	in	in	ADP
ejpam-5711	30	20	[	[	X
ejpam-5711	30	21	22	22	NUM
ejpam-5711	30	22	]	]	PUNCT
ejpam-5711	30	23	.	.	PUNCT
ejpam-5711	31	1	gutman	gutman	NOUN
ejpam-5711	31	2	and	and	CCONJ
ejpam-5711	31	3	trinajstić	trinajstić	NOUN
ejpam-5711	31	4	in	in	ADP
ejpam-5711	31	5	[	[	X
ejpam-5711	31	6	11	11	NUM
ejpam-5711	31	7	]	]	PUNCT
ejpam-5711	31	8	introduced	introduce	VERB
ejpam-5711	31	9	two	two	NUM
ejpam-5711	31	10	new	new	ADJ
ejpam-5711	31	11	indices	index	NOUN
ejpam-5711	31	12	labeled	label	VERB
ejpam-5711	31	13	as	as	ADP
ejpam-5711	31	14	the	the	DET
ejpam-5711	31	15	first	first	PROPN
ejpam-5711	31	16	zagreb	zagreb	PROPN
ejpam-5711	31	17	index	index	PROPN
ejpam-5711	31	18	,	,	PUNCT
ejpam-5711	31	19	denoted	denote	VERB
ejpam-5711	31	20	as	as	ADP
ejpam-5711	31	21	m1	m1	NOUN
ejpam-5711	31	22	,	,	PUNCT
ejpam-5711	31	23	and	and	CCONJ
ejpam-5711	31	24	the	the	DET
ejpam-5711	31	25	second	second	ADJ
ejpam-5711	31	26	zagreb	zagreb	PROPN
ejpam-5711	31	27	index	index	PROPN
ejpam-5711	31	28	,	,	PUNCT
ejpam-5711	31	29	denoted	denote	VERB
ejpam-5711	31	30	as	as	ADP
ejpam-5711	31	31	m2	m2	PROPN
ejpam-5711	31	32	,	,	PUNCT
ejpam-5711	31	33	defined	define	VERB
ejpam-5711	31	34	as	as	ADP
ejpam-5711	31	35	:	:	PUNCT
ejpam-5711	31	36	m1(h	m1(h	PROPN
ejpam-5711	31	37	)	)	PUNCT
ejpam-5711	31	38	=	=	SYM
ejpam-5711	31	39	∑	∑	PUNCT
ejpam-5711	31	40	uv∈e(h	uv∈e(h	NUM
ejpam-5711	31	41	)	)	PUNCT
ejpam-5711	31	42	(	(	PUNCT
ejpam-5711	31	43	du	du	PROPN
ejpam-5711	31	44	+	+	CCONJ
ejpam-5711	31	45	dv	dv	PROPN
ejpam-5711	31	46	)	)	PUNCT
ejpam-5711	31	47	,	,	PUNCT
ejpam-5711	31	48	m2(h	m2(h	PROPN
ejpam-5711	31	49	)	)	PUNCT
ejpam-5711	31	50	=	=	SYM
ejpam-5711	31	51	∑	∑	PUNCT
ejpam-5711	31	52	uv∈e(h	uv∈e(h	NUM
ejpam-5711	31	53	)	)	PUNCT
ejpam-5711	31	54	(	(	PUNCT
ejpam-5711	31	55	dudv	dudv	NOUN
ejpam-5711	31	56	)	)	PUNCT
ejpam-5711	31	57	.	.	PUNCT
ejpam-5711	32	1	nikolic	nikolic	PROPN
ejpam-5711	32	2	et	et	PROPN
ejpam-5711	32	3	al	al	PROPN
ejpam-5711	32	4	.	.	PUNCT
ejpam-5711	33	1	in	in	ADP
ejpam-5711	33	2	[	[	X
ejpam-5711	33	3	19	19	NUM
ejpam-5711	33	4	]	]	PUNCT
ejpam-5711	33	5	,	,	PUNCT
ejpam-5711	33	6	studied	study	VERB
ejpam-5711	33	7	a	a	DET
ejpam-5711	33	8	modified	modified	ADJ
ejpam-5711	33	9	second	second	ADJ
ejpam-5711	33	10	zagrab	zagrab	NOUN
ejpam-5711	33	11	index	index	NOUN
ejpam-5711	33	12	mm2	mm2	PROPN
ejpam-5711	33	13	,	,	PUNCT
ejpam-5711	33	14	formulated	formulate	VERB
ejpam-5711	33	15	as	as	ADP
ejpam-5711	33	16	:	:	PUNCT
ejpam-5711	33	17	mm2(h	mm2(h	PROPN
ejpam-5711	33	18	)	)	PUNCT
ejpam-5711	33	19	=	=	PUNCT
ejpam-5711	33	20	∑	∑	PUNCT
ejpam-5711	33	21	uv∈e(h	uv∈e(h	NUM
ejpam-5711	33	22	)	)	PUNCT
ejpam-5711	33	23	1	1	NUM
ejpam-5711	33	24	(	(	PUNCT
ejpam-5711	33	25	dudv	dudv	NOUN
ejpam-5711	33	26	)	)	PUNCT
ejpam-5711	33	27	.	.	PUNCT
ejpam-5711	34	1	randic	randic	ADJ
ejpam-5711	34	2	in	in	ADP
ejpam-5711	34	3	[	[	X
ejpam-5711	34	4	20	20	NUM
ejpam-5711	34	5	]	]	PUNCT
ejpam-5711	34	6	,	,	PUNCT
ejpam-5711	34	7	introduced	introduce	VERB
ejpam-5711	34	8	a	a	DET
ejpam-5711	34	9	bound	bind	VERB
ejpam-5711	34	10	-	-	PUNCT
ejpam-5711	34	11	additive	additive	ADJ
ejpam-5711	34	12	topological	topological	ADJ
ejpam-5711	34	13	index	index	NOUN
ejpam-5711	34	14	as	as	ADP
ejpam-5711	34	15	:	:	PUNCT
ejpam-5711	34	16	r−(1/2)(h	r−(1/2)(h	ADJ
ejpam-5711	34	17	)	)	PUNCT
ejpam-5711	34	18	=	=	PUNCT
ejpam-5711	34	19	∑	∑	PUNCT
ejpam-5711	34	20	uv∈e(h	uv∈e(h	NUM
ejpam-5711	34	21	)	)	PUNCT
ejpam-5711	34	22	1√	1√	ADJ
ejpam-5711	34	23	dudv	dudv	NOUN
ejpam-5711	34	24	.	.	PUNCT
ejpam-5711	35	1	n.	n.	PROPN
ejpam-5711	35	2	t.	t.	PROPN
ejpam-5711	35	3	sarhan	sarhan	PROPN
ejpam-5711	35	4	,	,	PUNCT
ejpam-5711	35	5	d.	d.	PROPN
ejpam-5711	35	6	a.	a.	PROPN
ejpam-5711	35	7	ali	ali	PROPN
ejpam-5711	35	8	,	,	PUNCT
ejpam-5711	35	9	g.	g.	PROPN
ejpam-5711	35	10	h.	h.	PROPN
ejpam-5711	36	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	36	2	/	/	SYM
ejpam-5711	36	3	eur	eur	PROPN
ejpam-5711	36	4	.	.	PUNCT
ejpam-5711	37	1	j.	j.	PROPN
ejpam-5711	37	2	pure	pure	PROPN
ejpam-5711	37	3	appl	appl	PROPN
ejpam-5711	37	4	.	.	PROPN
ejpam-5711	37	5	math	math	PROPN
ejpam-5711	37	6	,	,	PUNCT
ejpam-5711	37	7	18	18	NUM
ejpam-5711	37	8	(	(	PUNCT
ejpam-5711	37	9	1	1	NUM
ejpam-5711	37	10	)	)	PUNCT
ejpam-5711	37	11	(	(	PUNCT
ejpam-5711	37	12	2025	2025	NUM
ejpam-5711	37	13	)	)	PUNCT
ejpam-5711	37	14	,	,	PUNCT
ejpam-5711	37	15	5711	5711	NUM
ejpam-5711	37	16	3	3	NUM
ejpam-5711	37	17	of	of	ADP
ejpam-5711	37	18	15	15	NUM
ejpam-5711	37	19	the	the	DET
ejpam-5711	37	20	general	general	PROPN
ejpam-5711	37	21	randic	randic	ADJ
ejpam-5711	37	22	index	index	NOUN
ejpam-5711	37	23	was	be	AUX
ejpam-5711	37	24	introduced	introduce	VERB
ejpam-5711	37	25	by	by	ADP
ejpam-5711	37	26	bollobas	bollobas	PROPN
ejpam-5711	37	27	et	et	NOUN
ejpam-5711	37	28	.	.	PUNCT
ejpam-5711	38	1	al	al	PROPN
ejpam-5711	38	2	in	in	ADP
ejpam-5711	38	3	[	[	X
ejpam-5711	38	4	5	5	NUM
ejpam-5711	38	5	]	]	PUNCT
ejpam-5711	38	6	,	,	PUNCT
ejpam-5711	38	7	rγ(h	rγ(h	NOUN
ejpam-5711	38	8	)	)	PUNCT
ejpam-5711	38	9	=	=	SYM
ejpam-5711	38	10	∑	∑	PUNCT
ejpam-5711	38	11	uv∈e(h	uv∈e(h	NUM
ejpam-5711	38	12	)	)	PUNCT
ejpam-5711	38	13	(	(	PUNCT
ejpam-5711	38	14	dudv	dudv	NOUN
ejpam-5711	38	15	)	)	PUNCT
ejpam-5711	38	16	γ	γ	NOUN
ejpam-5711	38	17	.	.	PUNCT
ejpam-5711	39	1	another	another	DET
ejpam-5711	39	2	randic	randic	ADJ
ejpam-5711	39	3	index	index	NOUN
ejpam-5711	39	4	is	be	AUX
ejpam-5711	39	5	called	call	VERB
ejpam-5711	39	6	harmonic	harmonic	ADJ
ejpam-5711	39	7	index	index	NOUN
ejpam-5711	39	8	defined	define	VERB
ejpam-5711	39	9	by	by	ADP
ejpam-5711	39	10	fajtlowics	fajtlowic	NOUN
ejpam-5711	39	11	in	in	ADP
ejpam-5711	39	12	[	[	X
ejpam-5711	39	13	7	7	NUM
ejpam-5711	39	14	]	]	PUNCT
ejpam-5711	39	15	,	,	PUNCT
ejpam-5711	39	16	and	and	CCONJ
ejpam-5711	39	17	the	the	DET
ejpam-5711	39	18	inverse	inverse	NOUN
ejpam-5711	39	19	sum	sum	NOUN
ejpam-5711	39	20	index	index	NOUN
ejpam-5711	39	21	established	establish	VERB
ejpam-5711	39	22	by	by	ADP
ejpam-5711	39	23	vukicevic	vukicevic	NOUN
ejpam-5711	39	24	and	and	CCONJ
ejpam-5711	39	25	graovav	graovav	ADJ
ejpam-5711	39	26	in	in	ADP
ejpam-5711	39	27	[	[	X
ejpam-5711	39	28	21	21	NUM
ejpam-5711	39	29	]	]	PUNCT
ejpam-5711	39	30	,	,	PUNCT
ejpam-5711	39	31	h(h	h(h	X
ejpam-5711	39	32	)	)	PUNCT
ejpam-5711	39	33	=	=	SYM
ejpam-5711	39	34	∑	∑	PUNCT
ejpam-5711	39	35	uv∈e(h	uv∈e(h	NUM
ejpam-5711	39	36	)	)	PUNCT
ejpam-5711	39	37	2	2	NUM
ejpam-5711	39	38	du+dv	du+dv	NOUN
ejpam-5711	39	39	,	,	PUNCT
ejpam-5711	39	40	i(h	i(h	NOUN
ejpam-5711	39	41	)	)	PUNCT
ejpam-5711	39	42	=	=	PUNCT
ejpam-5711	39	43	∑	∑	PUNCT
ejpam-5711	39	44	uv∈e(h	uv∈e(h	NUM
ejpam-5711	39	45	)	)	PUNCT
ejpam-5711	40	1	dudv	dudv	ADP
ejpam-5711	40	2	du+dv	du+dv	NOUN
ejpam-5711	40	3	.	.	PUNCT
ejpam-5711	41	1	gupta	gupta	PROPN
ejpam-5711	41	2	et	et	PROPN
ejpam-5711	41	3	al	al	PROPN
ejpam-5711	41	4	.	.	PUNCT
ejpam-5711	42	1	[	[	X
ejpam-5711	42	2	9	9	NUM
ejpam-5711	42	3	]	]	PUNCT
ejpam-5711	42	4	introduced	introduce	VERB
ejpam-5711	42	5	symmetric	symmetric	ADJ
ejpam-5711	42	6	division	division	NOUN
ejpam-5711	42	7	degree	degree	NOUN
ejpam-5711	42	8	index	index	NOUN
ejpam-5711	42	9	ssd(h	ssd(h	PROPN
ejpam-5711	42	10	)	)	PUNCT
ejpam-5711	42	11	,	,	PUNCT
ejpam-5711	42	12	formulated	formulate	VERB
ejpam-5711	42	13	as	as	ADP
ejpam-5711	42	14	:	:	PUNCT
ejpam-5711	42	15	ssd(h	ssd(h	X
ejpam-5711	42	16	)	)	PUNCT
ejpam-5711	43	1	=	=	PUNCT
ejpam-5711	43	2	∑	∑	PUNCT
ejpam-5711	43	3	uv∈e(h	uv∈e(h	NUM
ejpam-5711	43	4	)	)	PUNCT
ejpam-5711	43	5	(	(	PUNCT
ejpam-5711	43	6	min(du	min(du	X
ejpam-5711	43	7	,	,	PUNCT
ejpam-5711	43	8	dv	dv	PROPN
ejpam-5711	43	9	)	)	PUNCT
ejpam-5711	43	10	max(du	max(du	PROPN
ejpam-5711	43	11	,	,	PUNCT
ejpam-5711	43	12	dv	dv	PROPN
ejpam-5711	43	13	)	)	PUNCT
ejpam-5711	43	14	+	+	NUM
ejpam-5711	43	15	max(du	max(du	NOUN
ejpam-5711	43	16	,	,	PUNCT
ejpam-5711	43	17	dv	dv	PROPN
ejpam-5711	43	18	)	)	PUNCT
ejpam-5711	43	19	min(du	min(du	PROPN
ejpam-5711	43	20	,	,	PUNCT
ejpam-5711	43	21	dv	dv	PROPN
ejpam-5711	43	22	)	)	PUNCT
ejpam-5711	43	23	)	)	PUNCT
ejpam-5711	43	24	.	.	PUNCT
ejpam-5711	44	1	computational	computational	ADJ
ejpam-5711	44	2	of	of	ADP
ejpam-5711	44	3	degree	degree	NOUN
ejpam-5711	44	4	-	-	PUNCT
ejpam-5711	44	5	based	base	VERB
ejpam-5711	44	6	topological	topological	ADJ
ejpam-5711	44	7	indices	index	NOUN
ejpam-5711	44	8	is	be	AUX
ejpam-5711	44	9	immediately	immediately	ADV
ejpam-5711	44	10	from	from	ADP
ejpam-5711	44	11	the	the	DET
ejpam-5711	44	12	rules	rule	NOUN
ejpam-5711	44	13	written	write	VERB
ejpam-5711	44	14	above	above	ADV
ejpam-5711	44	15	or	or	CCONJ
ejpam-5711	44	16	use	use	VERB
ejpam-5711	44	17	m	m	NOUN
ejpam-5711	44	18	-	-	NOUN
ejpam-5711	44	19	polynomial	polynomial	ADJ
ejpam-5711	44	20	with	with	ADP
ejpam-5711	44	21	next	next	ADJ
ejpam-5711	44	22	notations	notation	NOUN
ejpam-5711	44	23	to	to	PART
ejpam-5711	44	24	compute	compute	VERB
ejpam-5711	44	25	degree	degree	NOUN
ejpam-5711	44	26	-	-	PUNCT
ejpam-5711	44	27	based	base	VERB
ejpam-5711	44	28	topological	topological	ADJ
ejpam-5711	44	29	indices	index	NOUN
ejpam-5711	44	30	.	.	PUNCT
ejpam-5711	45	1	dx	dx	PROPN
ejpam-5711	46	1	=	=	PUNCT
ejpam-5711	46	2	x	x	SYM
ejpam-5711	46	3	∂m(h;x	∂m(h;x	PROPN
ejpam-5711	46	4	,	,	PUNCT
ejpam-5711	46	5	y	y	NOUN
ejpam-5711	46	6	)	)	PUNCT
ejpam-5711	46	7	∂x	∂x	PROPN
ejpam-5711	46	8	.	.	PUNCT
ejpam-5711	47	1	dy	dy	NOUN
ejpam-5711	47	2	=	=	PUNCT
ejpam-5711	47	3	y	y	PROPN
ejpam-5711	47	4	∂m(h;x	∂m(h;x	PROPN
ejpam-5711	47	5	,	,	PUNCT
ejpam-5711	47	6	y	y	NOUN
ejpam-5711	47	7	)	)	PUNCT
ejpam-5711	47	8	∂y	∂y	PROPN
ejpam-5711	47	9	.	.	PUNCT
ejpam-5711	48	1	sx	sx	PROPN
ejpam-5711	48	2	=	=	SYM
ejpam-5711	48	3	∫	∫	PROPN
ejpam-5711	48	4	x	x	SYM
ejpam-5711	48	5	0	0	NUM
ejpam-5711	48	6	m(h;x	m(h;x	PROPN
ejpam-5711	48	7	,	,	PUNCT
ejpam-5711	48	8	y	y	NOUN
ejpam-5711	48	9	)	)	PUNCT
ejpam-5711	48	10	t	t	PROPN
ejpam-5711	49	1	dt	dt	PROPN
ejpam-5711	49	2	.	.	PUNCT
ejpam-5711	50	1	sy	sy	PROPN
ejpam-5711	50	2	=	=	SYM
ejpam-5711	50	3	∫	∫	PROPN
ejpam-5711	50	4	y	y	PROPN
ejpam-5711	50	5	0	0	NUM
ejpam-5711	50	6	m(h;x	m(h;x	PROPN
ejpam-5711	50	7	,	,	PUNCT
ejpam-5711	50	8	y	y	NOUN
ejpam-5711	50	9	)	)	PUNCT
ejpam-5711	50	10	t	t	PROPN
ejpam-5711	51	1	dt	dt	PROPN
ejpam-5711	51	2	.	.	PUNCT
ejpam-5711	52	1	jm(h;x	jm(h;x	PROPN
ejpam-5711	52	2	,	,	PUNCT
ejpam-5711	52	3	y	y	NOUN
ejpam-5711	52	4	)	)	PUNCT
ejpam-5711	52	5	=	=	PUNCT
ejpam-5711	52	6	m(h;x	m(h;x	X
ejpam-5711	52	7	,	,	PUNCT
ejpam-5711	52	8	x	x	NOUN
ejpam-5711	52	9	)	)	PUNCT
ejpam-5711	52	10	.	.	PUNCT
ejpam-5711	53	1	2	2	X
ejpam-5711	53	2	.	.	X
ejpam-5711	53	3	main	main	ADJ
ejpam-5711	53	4	results	result	NOUN
ejpam-5711	53	5	this	this	DET
ejpam-5711	53	6	section	section	NOUN
ejpam-5711	53	7	comprises	comprise	VERB
ejpam-5711	53	8	three	three	NUM
ejpam-5711	53	9	subsections	subsection	NOUN
ejpam-5711	53	10	,	,	PUNCT
ejpam-5711	53	11	each	each	PRON
ejpam-5711	53	12	dedicated	dedicated	ADJ
ejpam-5711	53	13	to	to	ADP
ejpam-5711	53	14	distinct	distinct	ADJ
ejpam-5711	53	15	aspects	aspect	NOUN
ejpam-5711	53	16	of	of	ADP
ejpam-5711	53	17	our	our	PRON
ejpam-5711	53	18	analysis	analysis	NOUN
ejpam-5711	53	19	.	.	PUNCT
ejpam-5711	54	1	in	in	ADP
ejpam-5711	54	2	the	the	DET
ejpam-5711	54	3	first	first	ADJ
ejpam-5711	54	4	subsection	subsection	NOUN
ejpam-5711	54	5	,	,	PUNCT
ejpam-5711	54	6	we	we	PRON
ejpam-5711	54	7	investigate	investigate	VERB
ejpam-5711	54	8	the	the	DET
ejpam-5711	54	9	m	m	NOUN
ejpam-5711	54	10	-	-	ADJ
ejpam-5711	54	11	polynomial	polynomial	ADJ
ejpam-5711	54	12	and	and	CCONJ
ejpam-5711	54	13	degree	degree	NOUN
ejpam-5711	54	14	-	-	PUNCT
ejpam-5711	54	15	based	base	VERB
ejpam-5711	54	16	topological	topological	ADJ
ejpam-5711	54	17	indices	index	NOUN
ejpam-5711	54	18	associated	associate	VERB
ejpam-5711	54	19	with	with	ADP
ejpam-5711	54	20	the	the	DET
ejpam-5711	54	21	fractal	fractal	ADJ
ejpam-5711	54	22	growth	growth	NOUN
ejpam-5711	54	23	pattern	pattern	NOUN
ejpam-5711	54	24	of	of	ADP
ejpam-5711	54	25	benzene	benzene	NOUN
ejpam-5711	54	26	.	.	PUNCT
ejpam-5711	55	1	subsection	subsection	NOUN
ejpam-5711	55	2	two	two	NUM
ejpam-5711	55	3	presents	present	VERB
ejpam-5711	55	4	our	our	PRON
ejpam-5711	55	5	findings	finding	NOUN
ejpam-5711	55	6	on	on	ADP
ejpam-5711	55	7	the	the	DET
ejpam-5711	55	8	m	m	NOUN
ejpam-5711	55	9	-	-	ADJ
ejpam-5711	55	10	polynomial	polynomial	ADJ
ejpam-5711	55	11	of	of	ADP
ejpam-5711	55	12	pythagoras	pythagoras	PROPN
ejpam-5711	55	13	tree	tree	NOUN
ejpam-5711	55	14	as	as	ADV
ejpam-5711	55	15	well	well	ADV
ejpam-5711	55	16	as	as	ADP
ejpam-5711	55	17	the	the	DET
ejpam-5711	55	18	degree	degree	NOUN
ejpam-5711	55	19	-	-	PUNCT
ejpam-5711	55	20	based	base	VERB
ejpam-5711	55	21	topological	topological	ADJ
ejpam-5711	55	22	indices	index	NOUN
ejpam-5711	55	23	of	of	ADP
ejpam-5711	55	24	the	the	DET
ejpam-5711	55	25	pythagoras	pythagoras	PROPN
ejpam-5711	55	26	tree	tree	NOUN
ejpam-5711	55	27	.	.	PUNCT
ejpam-5711	56	1	finally	finally	ADV
ejpam-5711	56	2	,	,	PUNCT
ejpam-5711	56	3	we	we	PRON
ejpam-5711	56	4	explore	explore	VERB
ejpam-5711	56	5	the	the	DET
ejpam-5711	56	6	dendrimer	dendrimer	NOUN
ejpam-5711	56	7	of	of	ADP
ejpam-5711	56	8	benzene	benzene	NOUN
ejpam-5711	56	9	and	and	CCONJ
ejpam-5711	56	10	its	its	PRON
ejpam-5711	56	11	associated	associated	ADJ
ejpam-5711	56	12	topological	topological	ADJ
ejpam-5711	56	13	indices	index	NOUN
ejpam-5711	56	14	in	in	ADP
ejpam-5711	56	15	the	the	DET
ejpam-5711	56	16	concluding	conclude	VERB
ejpam-5711	56	17	subsection	subsection	NOUN
ejpam-5711	56	18	.	.	PUNCT
ejpam-5711	57	1	n.	n.	PROPN
ejpam-5711	57	2	t.	t.	PROPN
ejpam-5711	57	3	sarhan	sarhan	PROPN
ejpam-5711	57	4	,	,	PUNCT
ejpam-5711	57	5	d.	d.	PROPN
ejpam-5711	57	6	a.	a.	PROPN
ejpam-5711	57	7	ali	ali	PROPN
ejpam-5711	57	8	,	,	PUNCT
ejpam-5711	57	9	g.	g.	PROPN
ejpam-5711	57	10	h.	h.	PROPN
ejpam-5711	58	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	58	2	/	/	SYM
ejpam-5711	58	3	eur	eur	PROPN
ejpam-5711	58	4	.	.	PUNCT
ejpam-5711	59	1	j.	j.	PROPN
ejpam-5711	59	2	pure	pure	PROPN
ejpam-5711	59	3	appl	appl	PROPN
ejpam-5711	59	4	.	.	PROPN
ejpam-5711	59	5	math	math	PROPN
ejpam-5711	59	6	,	,	PUNCT
ejpam-5711	59	7	18	18	NUM
ejpam-5711	59	8	(	(	PUNCT
ejpam-5711	59	9	1	1	NUM
ejpam-5711	59	10	)	)	PUNCT
ejpam-5711	59	11	(	(	PUNCT
ejpam-5711	59	12	2025	2025	NUM
ejpam-5711	59	13	)	)	PUNCT
ejpam-5711	59	14	,	,	PUNCT
ejpam-5711	59	15	5711	5711	NUM
ejpam-5711	59	16	4	4	NUM
ejpam-5711	59	17	of	of	ADP
ejpam-5711	59	18	15	15	NUM
ejpam-5711	59	19	2.1	2.1	NUM
ejpam-5711	59	20	.	.	PUNCT
ejpam-5711	60	1	fractal	fractal	ADJ
ejpam-5711	60	2	growth	growth	NOUN
ejpam-5711	60	3	of	of	ADP
ejpam-5711	60	4	benzene	benzene	NOUN
ejpam-5711	60	5	the	the	DET
ejpam-5711	60	6	term	term	NOUN
ejpam-5711	60	7	fractal	fractal	NOUN
ejpam-5711	60	8	was	be	AUX
ejpam-5711	60	9	coined	coin	VERB
ejpam-5711	60	10	in	in	ADP
ejpam-5711	60	11	1975	1975	NUM
ejpam-5711	60	12	by	by	ADP
ejpam-5711	60	13	benoit	benoit	NOUN
ejpam-5711	60	14	mandelbrot	mandelbrot	PROPN
ejpam-5711	60	15	to	to	PART
ejpam-5711	60	16	describe	describe	VERB
ejpam-5711	60	17	a	a	DET
ejpam-5711	60	18	new	new	ADJ
ejpam-5711	60	19	idea	idea	NOUN
ejpam-5711	60	20	in	in	ADP
ejpam-5711	60	21	geometry	geometry	NOUN
ejpam-5711	60	22	.	.	PUNCT
ejpam-5711	61	1	geometric	geometric	ADJ
ejpam-5711	61	2	figures	figure	NOUN
ejpam-5711	61	3	in	in	ADP
ejpam-5711	61	4	regular	regular	ADJ
ejpam-5711	61	5	shapes	shape	NOUN
ejpam-5711	61	6	are	be	AUX
ejpam-5711	61	7	characterized	characterize	VERB
ejpam-5711	61	8	by	by	ADP
ejpam-5711	61	9	mathematical	mathematical	ADJ
ejpam-5711	61	10	equations	equation	NOUN
ejpam-5711	61	11	that	that	PRON
ejpam-5711	61	12	define	define	VERB
ejpam-5711	61	13	their	their	PRON
ejpam-5711	61	14	dimensions	dimension	NOUN
ejpam-5711	61	15	such	such	ADJ
ejpam-5711	61	16	as	as	ADP
ejpam-5711	61	17	length	length	NOUN
ejpam-5711	61	18	,	,	PUNCT
ejpam-5711	61	19	width	width	ADJ
ejpam-5711	61	20	,	,	PUNCT
ejpam-5711	61	21	and	and	CCONJ
ejpam-5711	61	22	height	height	NOUN
ejpam-5711	61	23	.	.	PUNCT
ejpam-5711	62	1	irregular	irregular	ADJ
ejpam-5711	62	2	shapes	shape	NOUN
ejpam-5711	62	3	can	can	AUX
ejpam-5711	62	4	not	not	PART
ejpam-5711	62	5	be	be	AUX
ejpam-5711	62	6	measured	measure	VERB
ejpam-5711	62	7	in	in	ADP
ejpam-5711	62	8	this	this	DET
ejpam-5711	62	9	way	way	NOUN
ejpam-5711	62	10	.	.	PUNCT
ejpam-5711	63	1	a	a	DET
ejpam-5711	63	2	fractal	fractal	NOUN
ejpam-5711	63	3	is	be	AUX
ejpam-5711	63	4	a	a	DET
ejpam-5711	63	5	type	type	NOUN
ejpam-5711	63	6	of	of	ADP
ejpam-5711	63	7	mathematical	mathematical	ADJ
ejpam-5711	63	8	shape	shape	NOUN
ejpam-5711	63	9	that	that	PRON
ejpam-5711	63	10	are	be	AUX
ejpam-5711	63	11	infinitely	infinitely	ADV
ejpam-5711	63	12	complex	complex	ADJ
ejpam-5711	63	13	.	.	PUNCT
ejpam-5711	64	1	in	in	ADP
ejpam-5711	64	2	essence	essence	NOUN
ejpam-5711	64	3	,	,	PUNCT
ejpam-5711	64	4	a	a	DET
ejpam-5711	64	5	fractal	fractal	NOUN
ejpam-5711	64	6	is	be	AUX
ejpam-5711	64	7	a	a	DET
ejpam-5711	64	8	pattern	pattern	NOUN
ejpam-5711	64	9	that	that	PRON
ejpam-5711	64	10	repeats	repeat	VERB
ejpam-5711	64	11	forever	forever	ADV
ejpam-5711	64	12	,	,	PUNCT
ejpam-5711	64	13	and	and	CCONJ
ejpam-5711	64	14	every	every	DET
ejpam-5711	64	15	part	part	NOUN
ejpam-5711	64	16	of	of	ADP
ejpam-5711	64	17	the	the	DET
ejpam-5711	64	18	fractal	fractal	NOUN
ejpam-5711	64	19	,	,	PUNCT
ejpam-5711	64	20	regardless	regardless	ADV
ejpam-5711	64	21	of	of	ADP
ejpam-5711	64	22	how	how	SCONJ
ejpam-5711	64	23	zoomed	zoom	VERB
ejpam-5711	64	24	in	in	ADV
ejpam-5711	64	25	,	,	PUNCT
ejpam-5711	64	26	or	or	CCONJ
ejpam-5711	64	27	zoomed	zoom	VERB
ejpam-5711	64	28	out	out	ADP
ejpam-5711	64	29	you	you	PRON
ejpam-5711	64	30	are	be	AUX
ejpam-5711	64	31	,	,	PUNCT
ejpam-5711	64	32	it	it	PRON
ejpam-5711	64	33	looks	look	VERB
ejpam-5711	64	34	very	very	ADV
ejpam-5711	64	35	similar	similar	ADJ
ejpam-5711	64	36	to	to	ADP
ejpam-5711	64	37	the	the	DET
ejpam-5711	64	38	whole	whole	ADJ
ejpam-5711	64	39	image	image	NOUN
ejpam-5711	64	40	.	.	PUNCT
ejpam-5711	65	1	fractals	fractal	NOUN
ejpam-5711	65	2	are	be	AUX
ejpam-5711	65	3	currently	currently	ADV
ejpam-5711	65	4	employed	employ	VERB
ejpam-5711	65	5	in	in	ADP
ejpam-5711	65	6	various	various	ADJ
ejpam-5711	65	7	applications	application	NOUN
ejpam-5711	65	8	to	to	PART
ejpam-5711	65	9	generate	generate	VERB
ejpam-5711	65	10	textured	textured	ADJ
ejpam-5711	65	11	landscapes	landscape	NOUN
ejpam-5711	65	12	and	and	CCONJ
ejpam-5711	65	13	images	image	NOUN
ejpam-5711	65	14	resembling	resemble	VERB
ejpam-5711	65	15	natural	natural	ADJ
ejpam-5711	65	16	scenes	scene	NOUN
ejpam-5711	65	17	,	,	PUNCT
ejpam-5711	65	18	including	include	VERB
ejpam-5711	65	19	lunar	lunar	ADJ
ejpam-5711	65	20	surfaces	surface	NOUN
ejpam-5711	65	21	and	and	CCONJ
ejpam-5711	65	22	mountain	mountain	NOUN
ejpam-5711	65	23	ranges	range	NOUN
ejpam-5711	65	24	[	[	X
ejpam-5711	65	25	4	4	NUM
ejpam-5711	65	26	,	,	PUNCT
ejpam-5711	65	27	16	16	NUM
ejpam-5711	65	28	]	]	PUNCT
ejpam-5711	65	29	.	.	PUNCT
ejpam-5711	66	1	moreover	moreover	ADV
ejpam-5711	66	2	,	,	PUNCT
ejpam-5711	66	3	the	the	DET
ejpam-5711	66	4	order	order	NOUN
ejpam-5711	66	5	and	and	CCONJ
ejpam-5711	66	6	size	size	NOUN
ejpam-5711	66	7	of	of	ADP
ejpam-5711	66	8	all	all	DET
ejpam-5711	66	9	graphs	graph	NOUN
ejpam-5711	66	10	is	be	AUX
ejpam-5711	66	11	given	give	VERB
ejpam-5711	66	12	by	by	ADP
ejpam-5711	66	13	geometric	geometric	ADJ
ejpam-5711	66	14	series	series	NOUN
ejpam-5711	66	15	.	.	PUNCT
ejpam-5711	67	1	figure	figure	NOUN
ejpam-5711	67	2	1	1	NUM
ejpam-5711	67	3	:	:	PUNCT
ejpam-5711	67	4	fractal	fractal	ADJ
ejpam-5711	67	5	growth	growth	NOUN
ejpam-5711	67	6	of	of	ADP
ejpam-5711	67	7	benzene	benzene	NOUN
ejpam-5711	67	8	fgb1	fgb1	NOUN
ejpam-5711	67	9	,	,	PUNCT
ejpam-5711	67	10	fgb2	fgb2	PROPN
ejpam-5711	67	11	,	,	PUNCT
ejpam-5711	67	12	fgb3	fgb3	PROPN
ejpam-5711	67	13	and	and	CCONJ
ejpam-5711	67	14	fgb4	fgb4	PROPN
ejpam-5711	67	15	.	.	PUNCT
ejpam-5711	68	1	the	the	DET
ejpam-5711	68	2	following	follow	VERB
ejpam-5711	68	3	theorem	theorem	NOUN
ejpam-5711	68	4	computes	compute	VERB
ejpam-5711	68	5	the	the	DET
ejpam-5711	68	6	m	m	NOUN
ejpam-5711	68	7	-	-	ADJ
ejpam-5711	68	8	polynomial	polynomial	ADJ
ejpam-5711	68	9	of	of	ADP
ejpam-5711	68	10	fractal	fractal	ADJ
ejpam-5711	68	11	growth	growth	NOUN
ejpam-5711	68	12	of	of	ADP
ejpam-5711	68	13	benzene	benzene	NOUN
ejpam-5711	68	14	.	.	PUNCT
ejpam-5711	69	1	theorem	theorem	NOUN
ejpam-5711	69	2	1	1	NUM
ejpam-5711	69	3	.	.	PUNCT
ejpam-5711	70	1	let	let	AUX
ejpam-5711	70	2	fgbn	fgbn	NOUN
ejpam-5711	70	3	be	be	AUX
ejpam-5711	70	4	a	a	DET
ejpam-5711	70	5	fractal	fractal	ADJ
ejpam-5711	70	6	growth	growth	NOUN
ejpam-5711	70	7	of	of	ADP
ejpam-5711	70	8	benzene	benzene	NOUN
ejpam-5711	70	9	where	where	SCONJ
ejpam-5711	70	10	n	n	PRON
ejpam-5711	70	11	is	be	AUX
ejpam-5711	70	12	the	the	DET
ejpam-5711	70	13	number	number	NOUN
ejpam-5711	70	14	of	of	ADP
ejpam-5711	70	15	iterative	iterative	ADJ
ejpam-5711	70	16	fractal	fractal	ADJ
ejpam-5711	70	17	growth	growth	NOUN
ejpam-5711	70	18	.	.	PUNCT
ejpam-5711	71	1	(	(	PUNCT
ejpam-5711	71	2	i	i	NOUN
ejpam-5711	71	3	)	)	PUNCT
ejpam-5711	71	4	if	if	SCONJ
ejpam-5711	71	5	n	n	NOUN
ejpam-5711	71	6	=	=	SYM
ejpam-5711	71	7	1	1	NUM
ejpam-5711	71	8	,	,	PUNCT
ejpam-5711	71	9	then	then	ADV
ejpam-5711	71	10	m(fgb1;x	m(fgb1;x	PROPN
ejpam-5711	71	11	,	,	PUNCT
ejpam-5711	71	12	y	y	NOUN
ejpam-5711	71	13	)	)	PUNCT
ejpam-5711	71	14	=	=	SYM
ejpam-5711	71	15	6x2y2	6x2y2	NUM
ejpam-5711	71	16	.	.	PUNCT
ejpam-5711	72	1	(	(	PUNCT
ejpam-5711	72	2	ii	ii	NOUN
ejpam-5711	72	3	)	)	PUNCT
ejpam-5711	72	4	if	if	SCONJ
ejpam-5711	72	5	n	n	PRON
ejpam-5711	72	6	≥	≥	NOUN
ejpam-5711	72	7	2	2	NUM
ejpam-5711	72	8	,	,	PUNCT
ejpam-5711	72	9	then	then	ADV
ejpam-5711	72	10	m(fgbn;x	m(fgbn;x	PROPN
ejpam-5711	72	11	,	,	PUNCT
ejpam-5711	72	12	y	y	PROPN
ejpam-5711	72	13	)	)	PUNCT
ejpam-5711	72	14	=	=	PUNCT
ejpam-5711	73	1	[	[	X
ejpam-5711	73	2	20(7n−2	20(7n−2	NUM
ejpam-5711	73	3	)	)	PUNCT
ejpam-5711	74	1	+	+	CCONJ
ejpam-5711	74	2	4]x2y2	4]x2y2	NUM
ejpam-5711	75	1	+	+	CCONJ
ejpam-5711	76	1	[	[	X
ejpam-5711	76	2	16(7n−2)−	16(7n−2)−	NUM
ejpam-5711	76	3	4]x2y4	4]x2y4	NUM
ejpam-5711	76	4	+6(7n−2)x4y4	+6(7n−2)x4y4	NOUN
ejpam-5711	76	5	.	.	PUNCT
ejpam-5711	77	1	proof	proof	NOUN
ejpam-5711	77	2	.	.	PUNCT
ejpam-5711	78	1	assume	assume	VERB
ejpam-5711	78	2	that	that	SCONJ
ejpam-5711	78	3	fgbn	fgbn	NOUN
ejpam-5711	78	4	is	be	AUX
ejpam-5711	78	5	the	the	DET
ejpam-5711	78	6	fractal	fractal	ADJ
ejpam-5711	78	7	growth	growth	NOUN
ejpam-5711	78	8	of	of	ADP
ejpam-5711	78	9	benzene	benzene	NOUN
ejpam-5711	78	10	as	as	SCONJ
ejpam-5711	78	11	shown	show	VERB
ejpam-5711	78	12	in	in	ADP
ejpam-5711	78	13	figure	figure	NOUN
ejpam-5711	78	14	4	4	NUM
ejpam-5711	78	15	,	,	PUNCT
ejpam-5711	79	1	|v(fgbn)|	|v(fgbn)|	PROPN
ejpam-5711	79	2	=	=	SYM
ejpam-5711	79	3	|v(fgbn−1)|+6|v(fgbn−1)−	|v(fgbn−1)|+6|v(fgbn−1)−	PROPN
ejpam-5711	79	4	1|	1|	NUM
ejpam-5711	79	5	and	and	CCONJ
ejpam-5711	79	6	|e(fgbn)|	|e(fgbn)|	PROPN
ejpam-5711	79	7	=	=	PUNCT
ejpam-5711	79	8	6(7n−1	6(7n−1	NUM
ejpam-5711	79	9	)	)	PUNCT
ejpam-5711	79	10	,	,	PUNCT
ejpam-5711	79	11	where	where	SCONJ
ejpam-5711	79	12	n	n	PRON
ejpam-5711	79	13	≥	≥	NOUN
ejpam-5711	79	14	2	2	NUM
ejpam-5711	79	15	.	.	PUNCT
ejpam-5711	79	16	n.	n.	PROPN
ejpam-5711	79	17	t.	t.	PROPN
ejpam-5711	79	18	sarhan	sarhan	PROPN
ejpam-5711	79	19	,	,	PUNCT
ejpam-5711	79	20	d.	d.	PROPN
ejpam-5711	79	21	a.	a.	PROPN
ejpam-5711	79	22	ali	ali	PROPN
ejpam-5711	79	23	,	,	PUNCT
ejpam-5711	80	1	g.	g.	PROPN
ejpam-5711	80	2	h.	h.	PROPN
ejpam-5711	80	3	mohiaddin	mohiaddin	PROPN
ejpam-5711	80	4	/	/	SYM
ejpam-5711	80	5	eur	eur	PROPN
ejpam-5711	80	6	.	.	PUNCT
ejpam-5711	81	1	j.	j.	PROPN
ejpam-5711	81	2	pure	pure	PROPN
ejpam-5711	81	3	appl	appl	PROPN
ejpam-5711	81	4	.	.	PROPN
ejpam-5711	81	5	math	math	PROPN
ejpam-5711	81	6	,	,	PUNCT
ejpam-5711	81	7	18	18	NUM
ejpam-5711	81	8	(	(	PUNCT
ejpam-5711	81	9	1	1	NUM
ejpam-5711	81	10	)	)	PUNCT
ejpam-5711	81	11	(	(	PUNCT
ejpam-5711	81	12	2025	2025	NUM
ejpam-5711	81	13	)	)	PUNCT
ejpam-5711	81	14	,	,	PUNCT
ejpam-5711	81	15	5711	5711	NUM
ejpam-5711	81	16	5	5	NUM
ejpam-5711	81	17	of	of	ADP
ejpam-5711	81	18	15	15	NUM
ejpam-5711	81	19	(	(	PUNCT
ejpam-5711	81	20	i	i	NOUN
ejpam-5711	81	21	)	)	PUNCT
ejpam-5711	81	22	for	for	ADP
ejpam-5711	81	23	n	n	NOUN
ejpam-5711	81	24	=	=	SYM
ejpam-5711	81	25	1	1	NUM
ejpam-5711	81	26	,	,	PUNCT
ejpam-5711	81	27	the	the	DET
ejpam-5711	81	28	edge	edge	NOUN
ejpam-5711	81	29	set	set	VERB
ejpam-5711	81	30	e(fgb1	e(fgb1	PRON
ejpam-5711	81	31	)	)	PUNCT
ejpam-5711	81	32	has	have	VERB
ejpam-5711	81	33	only	only	ADV
ejpam-5711	81	34	one	one	NUM
ejpam-5711	81	35	partition	partition	NOUN
ejpam-5711	81	36	|e(2	|e(2	NOUN
ejpam-5711	81	37	,	,	PUNCT
ejpam-5711	81	38	2)|	2)|	NUM
ejpam-5711	81	39	=	=	SYM
ejpam-5711	81	40	|e	|e	NOUN
ejpam-5711	81	41	=	=	PUNCT
ejpam-5711	81	42	uv	uv	NOUN
ejpam-5711	81	43	∈	∈	PROPN
ejpam-5711	81	44	e(fgb1	e(fgb1	NUM
ejpam-5711	81	45	)	)	PUNCT
ejpam-5711	81	46	:	:	PUNCT
ejpam-5711	82	1	du	du	PROPN
ejpam-5711	82	2	=	=	SYM
ejpam-5711	82	3	2anddv	2anddv	NUM
ejpam-5711	82	4	=	=	SYM
ejpam-5711	82	5	2|	2|	NUM
ejpam-5711	82	6	=	=	SYM
ejpam-5711	82	7	6	6	NUM
ejpam-5711	82	8	.	.	PUNCT
ejpam-5711	83	1	hence	hence	ADV
ejpam-5711	83	2	,	,	PUNCT
ejpam-5711	83	3	the	the	DET
ejpam-5711	83	4	m	m	NOUN
ejpam-5711	83	5	-	-	NOUN
ejpam-5711	83	6	polynomial	polynomial	ADJ
ejpam-5711	83	7	for	for	ADP
ejpam-5711	83	8	fgb1	fgb1	NOUN
ejpam-5711	83	9	is	be	AUX
ejpam-5711	83	10	m(fgb1;x	m(fgb1;x	NOUN
ejpam-5711	83	11	,	,	PUNCT
ejpam-5711	83	12	y	y	NOUN
ejpam-5711	83	13	)	)	PUNCT
ejpam-5711	83	14	=	=	PUNCT
ejpam-5711	83	15	∑	∑	PUNCT
ejpam-5711	83	16	δ≤α≤β≤∆	δ≤α≤β≤∆	PROPN
ejpam-5711	83	17	mα	mα	PROPN
ejpam-5711	83	18	,	,	PUNCT
ejpam-5711	83	19	βx	βx	AUX
ejpam-5711	83	20	αyβ	αyβ	VERB
ejpam-5711	83	21	=	=	PUNCT
ejpam-5711	83	22	∑	∑	PUNCT
ejpam-5711	83	23	2≤2	2≤2	NUM
ejpam-5711	83	24	m2,2x	m2,2x	PROPN
ejpam-5711	83	25	2y2	2y2	NUM
ejpam-5711	83	26	=	=	SYM
ejpam-5711	83	27	6x2y2	6x2y2	NUM
ejpam-5711	83	28	.	.	PUNCT
ejpam-5711	84	1	(	(	PUNCT
ejpam-5711	84	2	ii	ii	NOUN
ejpam-5711	84	3	)	)	PUNCT
ejpam-5711	84	4	for	for	ADP
ejpam-5711	84	5	n	n	X
ejpam-5711	84	6	≥	≥	NUM
ejpam-5711	84	7	2	2	NUM
ejpam-5711	84	8	,	,	PUNCT
ejpam-5711	84	9	the	the	DET
ejpam-5711	84	10	edge	edge	NOUN
ejpam-5711	84	11	set	set	VERB
ejpam-5711	84	12	e(fgbn	e(fgbn	NOUN
ejpam-5711	84	13	)	)	PUNCT
ejpam-5711	84	14	can	can	AUX
ejpam-5711	84	15	be	be	AUX
ejpam-5711	84	16	divided	divide	VERB
ejpam-5711	84	17	into	into	ADP
ejpam-5711	84	18	the	the	DET
ejpam-5711	84	19	following	follow	VERB
ejpam-5711	84	20	three	three	NUM
ejpam-5711	84	21	parts	part	NOUN
ejpam-5711	84	22	|e(2	|e(2	NOUN
ejpam-5711	84	23	,	,	PUNCT
ejpam-5711	84	24	2)|	2)|	NUM
ejpam-5711	84	25	=	=	SYM
ejpam-5711	84	26	|e	|e	NOUN
ejpam-5711	84	27	=	=	PUNCT
ejpam-5711	84	28	uv	uv	NOUN
ejpam-5711	84	29	∈	∈	PROPN
ejpam-5711	84	30	e(fgbn	e(fgbn	NOUN
ejpam-5711	84	31	)	)	PUNCT
ejpam-5711	84	32	:	:	PUNCT
ejpam-5711	84	33	du	du	PROPN
ejpam-5711	84	34	=	=	SYM
ejpam-5711	84	35	2	2	NUM
ejpam-5711	84	36	and	and	CCONJ
ejpam-5711	84	37	dv	dv	PROPN
ejpam-5711	85	1	=	=	PROPN
ejpam-5711	85	2	2|	2|	NUM
ejpam-5711	85	3	=	=	SYM
ejpam-5711	86	1	20(7n−2	20(7n−2	NUM
ejpam-5711	86	2	)	)	PUNCT
ejpam-5711	86	3	+	+	CCONJ
ejpam-5711	86	4	4	4	NUM
ejpam-5711	86	5	,	,	PUNCT
ejpam-5711	86	6	|e(2	|e(2	NOUN
ejpam-5711	86	7	,	,	PUNCT
ejpam-5711	86	8	4)|	4)|	NUM
ejpam-5711	86	9	=	=	SYM
ejpam-5711	86	10	|e	|e	NOUN
ejpam-5711	87	1	=	=	PUNCT
ejpam-5711	87	2	uv	uv	NOUN
ejpam-5711	87	3	∈	∈	PROPN
ejpam-5711	87	4	e(fgbn	e(fgbn	NOUN
ejpam-5711	87	5	)	)	PUNCT
ejpam-5711	87	6	:	:	PUNCT
ejpam-5711	87	7	du	du	PROPN
ejpam-5711	87	8	=	=	SYM
ejpam-5711	87	9	2	2	NUM
ejpam-5711	87	10	and	and	CCONJ
ejpam-5711	87	11	dv	dv	PROPN
ejpam-5711	87	12	=	=	SYM
ejpam-5711	87	13	4|	4|	NUM
ejpam-5711	87	14	=	=	SYM
ejpam-5711	87	15	16(7n−2	16(7n−2	NUM
ejpam-5711	87	16	)	)	PUNCT
ejpam-5711	87	17	−	−	PROPN
ejpam-5711	87	18	4	4	NUM
ejpam-5711	87	19	,	,	PUNCT
ejpam-5711	87	20	and	and	CCONJ
ejpam-5711	87	21	|e(4	|e(4	NOUN
ejpam-5711	87	22	,	,	PUNCT
ejpam-5711	87	23	4)|	4)|	NUM
ejpam-5711	87	24	=	=	SYM
ejpam-5711	87	25	|e	|e	NOUN
ejpam-5711	88	1	=	=	PUNCT
ejpam-5711	88	2	uv	uv	NOUN
ejpam-5711	88	3	∈	∈	PROPN
ejpam-5711	88	4	e(fgbn	e(fgbn	NOUN
ejpam-5711	88	5	)	)	PUNCT
ejpam-5711	88	6	:	:	PUNCT
ejpam-5711	89	1	du	du	PROPN
ejpam-5711	89	2	=	=	SYM
ejpam-5711	89	3	4	4	NUM
ejpam-5711	89	4	and	and	CCONJ
ejpam-5711	89	5	dv	dv	PROPN
ejpam-5711	89	6	=	=	SYM
ejpam-5711	89	7	4|	4|	NUM
ejpam-5711	89	8	=	=	SYM
ejpam-5711	89	9	6(7n−2	6(7n−2	X
ejpam-5711	89	10	)	)	PUNCT
ejpam-5711	89	11	.	.	PUNCT
ejpam-5711	90	1	hence	hence	ADV
ejpam-5711	90	2	,	,	PUNCT
ejpam-5711	90	3	the	the	DET
ejpam-5711	90	4	m	m	NOUN
ejpam-5711	90	5	-	-	ADJ
ejpam-5711	90	6	polynomial	polynomial	ADJ
ejpam-5711	90	7	of	of	ADP
ejpam-5711	90	8	fgbn	fgbn	NOUN
ejpam-5711	90	9	is	be	AUX
ejpam-5711	90	10	m(fgbn;x	m(fgbn;x	PROPN
ejpam-5711	90	11	,	,	PUNCT
ejpam-5711	90	12	y	y	NOUN
ejpam-5711	90	13	)	)	PUNCT
ejpam-5711	90	14	=	=	PUNCT
ejpam-5711	90	15	∑	∑	PUNCT
ejpam-5711	90	16	δ≤α≤β≤∆	δ≤α≤β≤∆	PROPN
ejpam-5711	90	17	mα	mα	PROPN
ejpam-5711	90	18	,	,	PUNCT
ejpam-5711	90	19	βx	βx	AUX
ejpam-5711	90	20	αyβ	αyβ	VERB
ejpam-5711	90	21	=	=	PUNCT
ejpam-5711	90	22	∑	∑	PUNCT
ejpam-5711	90	23	2≤2	2≤2	NUM
ejpam-5711	90	24	m2,2x	m2,2x	NOUN
ejpam-5711	90	25	2y2	2y2	NUM
ejpam-5711	90	26	+	+	CCONJ
ejpam-5711	90	27	∑	∑	PUNCT
ejpam-5711	90	28	2≤4	2≤4	SYM
ejpam-5711	90	29	m2,4x	m2,4x	PROPN
ejpam-5711	90	30	2y4	2y4	NUM
ejpam-5711	91	1	+	+	CCONJ
ejpam-5711	91	2	∑	∑	PUNCT
ejpam-5711	91	3	4≤4	4≤4	NUM
ejpam-5711	91	4	m4,4x	m4,4x	PROPN
ejpam-5711	91	5	4y4	4y4	NUM
ejpam-5711	92	1	=	=	PUNCT
ejpam-5711	93	1	[	[	X
ejpam-5711	93	2	20(7n−2	20(7n−2	NUM
ejpam-5711	93	3	)	)	PUNCT
ejpam-5711	94	1	+	+	CCONJ
ejpam-5711	94	2	4]x2y2	4]x2y2	NUM
ejpam-5711	95	1	+	+	CCONJ
ejpam-5711	96	1	[	[	X
ejpam-5711	96	2	16(7n−2)−	16(7n−2)−	NUM
ejpam-5711	96	3	4]x2y4	4]x2y4	NUM
ejpam-5711	96	4	+	+	CCONJ
ejpam-5711	96	5	6(7n−2)x4y4	6(7n−2)x4y4	NOUN
ejpam-5711	96	6	.	.	PUNCT
ejpam-5711	96	7	degree	degree	NOUN
ejpam-5711	96	8	-	-	PUNCT
ejpam-5711	96	9	based	base	VERB
ejpam-5711	96	10	topological	topological	ADJ
ejpam-5711	96	11	indices	index	NOUN
ejpam-5711	96	12	of	of	ADP
ejpam-5711	96	13	fractal	fractal	ADJ
ejpam-5711	96	14	growth	growth	NOUN
ejpam-5711	96	15	of	of	ADP
ejpam-5711	96	16	benzene	benzene	ADJ
ejpam-5711	96	17	fgbn	fgbn	NOUN
ejpam-5711	96	18	,	,	PUNCT
ejpam-5711	96	19	n	n	PRON
ejpam-5711	96	20	≥	≥	NOUN
ejpam-5711	96	21	2	2	NUM
ejpam-5711	96	22	are	be	AUX
ejpam-5711	96	23	given	give	VERB
ejpam-5711	96	24	in	in	ADP
ejpam-5711	96	25	the	the	DET
ejpam-5711	96	26	next	next	ADJ
ejpam-5711	96	27	proposition	proposition	NOUN
ejpam-5711	96	28	.	.	PUNCT
ejpam-5711	97	1	proposition	proposition	NOUN
ejpam-5711	97	2	1	1	NUM
ejpam-5711	97	3	.	.	PUNCT
ejpam-5711	98	1	let	let	VERB
ejpam-5711	98	2	fgbn	fgbn	NOUN
ejpam-5711	98	3	be	be	AUX
ejpam-5711	98	4	a	a	DET
ejpam-5711	98	5	fractal	fractal	ADJ
ejpam-5711	98	6	growth	growth	NOUN
ejpam-5711	98	7	of	of	ADP
ejpam-5711	98	8	benzene	benzene	NOUN
ejpam-5711	98	9	where	where	SCONJ
ejpam-5711	98	10	n	n	PRON
ejpam-5711	98	11	≥	≥	NOUN
ejpam-5711	98	12	2	2	NUM
ejpam-5711	98	13	,	,	PUNCT
ejpam-5711	98	14	then	then	ADV
ejpam-5711	98	15	(	(	PUNCT
ejpam-5711	98	16	i	i	NOUN
ejpam-5711	98	17	)	)	PUNCT
ejpam-5711	98	18	m1(fgbn	m1(fgbn	NOUN
ejpam-5711	98	19	)	)	PUNCT
ejpam-5711	98	20	=	=	PUNCT
ejpam-5711	99	1	32(7n−1)−	32(7n−1)−	NUM
ejpam-5711	99	2	8	8	NUM
ejpam-5711	99	3	.	.	PUNCT
ejpam-5711	100	1	(	(	PUNCT
ejpam-5711	100	2	ii	ii	NOUN
ejpam-5711	100	3	)	)	PUNCT
ejpam-5711	100	4	m2(fgbn	m2(fgbn	NOUN
ejpam-5711	100	5	)	)	PUNCT
ejpam-5711	101	1	=	=	PUNCT
ejpam-5711	102	1	304(7n−2)−	304(7n−2)−	NUM
ejpam-5711	102	2	16	16	NUM
ejpam-5711	102	3	.	.	PUNCT
ejpam-5711	103	1	(	(	PUNCT
ejpam-5711	103	2	iii	iii	NOUN
ejpam-5711	103	3	)	)	PUNCT
ejpam-5711	103	4	mm2(fgbn	mm2(fgbn	NOUN
ejpam-5711	103	5	)	)	PUNCT
ejpam-5711	104	1	=	=	SYM
ejpam-5711	104	2	59	59	NUM
ejpam-5711	104	3	8	8	NUM
ejpam-5711	104	4	(	(	PUNCT
ejpam-5711	104	5	7	7	NUM
ejpam-5711	104	6	n−2	n−2	PROPN
ejpam-5711	104	7	)	)	PUNCT
ejpam-5711	104	8	+	+	CCONJ
ejpam-5711	104	9	1	1	NUM
ejpam-5711	104	10	2	2	NUM
ejpam-5711	104	11	.	.	PUNCT
ejpam-5711	104	12	(	(	PUNCT
ejpam-5711	104	13	iv	iv	X
ejpam-5711	104	14	)	)	PUNCT
ejpam-5711	104	15	rγ(fgbn	rγ(fgbn	PROPN
ejpam-5711	104	16	)	)	PUNCT
ejpam-5711	104	17	=	=	PUNCT
ejpam-5711	105	1	[	[	X
ejpam-5711	105	2	5(22γ+2	5(22γ+2	NUM
ejpam-5711	105	3	)	)	PUNCT
ejpam-5711	106	1	+	+	NUM
ejpam-5711	106	2	23γ+4	23γ+4	NUM
ejpam-5711	106	3	+	+	CCONJ
ejpam-5711	106	4	3(24γ+1)](7n−2	3(24γ+1)](7n−2	NUM
ejpam-5711	106	5	)	)	PUNCT
ejpam-5711	106	6	+	+	NUM
ejpam-5711	106	7	22γ+2	22γ+2	NUM
ejpam-5711	106	8	−	−	PROPN
ejpam-5711	106	9	23γ+2	23γ+2	NUM
ejpam-5711	106	10	.	.	PUNCT
ejpam-5711	107	1	(	(	PUNCT
ejpam-5711	107	2	v	v	NOUN
ejpam-5711	107	3	)	)	PUNCT
ejpam-5711	107	4	ssd(fgbn	ssd(fgbn	NOUN
ejpam-5711	107	5	)	)	PUNCT
ejpam-5711	107	6	=	=	SYM
ejpam-5711	108	1	92(7n−2)−	92(7n−2)−	NUM
ejpam-5711	108	2	2	2	NUM
ejpam-5711	108	3	.	.	PUNCT
ejpam-5711	108	4	(	(	PUNCT
ejpam-5711	108	5	vi	vi	NOUN
ejpam-5711	108	6	)	)	PUNCT
ejpam-5711	108	7	h(fgbn	h(fgbn	NOUN
ejpam-5711	108	8	)	)	PUNCT
ejpam-5711	109	1	=	=	PUNCT
ejpam-5711	110	1	101	101	NUM
ejpam-5711	110	2	6	6	NUM
ejpam-5711	110	3	(	(	PUNCT
ejpam-5711	110	4	7n−2	7n−2	NUM
ejpam-5711	110	5	)	)	PUNCT
ejpam-5711	110	6	+	+	CCONJ
ejpam-5711	110	7	2	2	NUM
ejpam-5711	110	8	3	3	NUM
ejpam-5711	110	9	.	.	PUNCT
ejpam-5711	111	1	(	(	PUNCT
ejpam-5711	111	2	vii	vii	PROPN
ejpam-5711	111	3	)	)	PUNCT
ejpam-5711	111	4	i(fgbn	i(fgbn	NOUN
ejpam-5711	111	5	)	)	PUNCT
ejpam-5711	112	1	=	=	PUNCT
ejpam-5711	112	2	160	160	NUM
ejpam-5711	112	3	3	3	NUM
ejpam-5711	112	4	(	(	PUNCT
ejpam-5711	112	5	7n−2)−	7n−2)−	NUM
ejpam-5711	112	6	4	4	NUM
ejpam-5711	112	7	3	3	NUM
ejpam-5711	112	8	.	.	PUNCT
ejpam-5711	113	1	proof	proof	NOUN
ejpam-5711	113	2	.	.	PUNCT
ejpam-5711	114	1	since	since	SCONJ
ejpam-5711	114	2	,	,	PUNCT
ejpam-5711	114	3	m(fgbn;x	m(fgbn;x	PROPN
ejpam-5711	114	4	,	,	PUNCT
ejpam-5711	114	5	y	y	PROPN
ejpam-5711	114	6	)	)	PUNCT
ejpam-5711	114	7	=	=	PUNCT
ejpam-5711	115	1	[	[	PUNCT
ejpam-5711	115	2	20(7n−2)+4]x2y2+[16(7n−2)−	20(7n−2)+4]x2y2+[16(7n−2)−	NUM
ejpam-5711	115	3	4]x2y4	4]x2y4	NUM
ejpam-5711	115	4	+	+	NOUN
ejpam-5711	115	5	6(7n−2)x4y4	6(7n−2)x4y4	NOUN
ejpam-5711	115	6	,	,	PUNCT
ejpam-5711	115	7	using	use	VERB
ejpam-5711	115	8	above	above	ADP
ejpam-5711	115	9	operators	operator	NOUN
ejpam-5711	115	10	we	we	PRON
ejpam-5711	115	11	get	get	VERB
ejpam-5711	115	12	:	:	PUNCT
ejpam-5711	115	13	n.	n.	PROPN
ejpam-5711	115	14	t.	t.	PROPN
ejpam-5711	115	15	sarhan	sarhan	PROPN
ejpam-5711	115	16	,	,	PUNCT
ejpam-5711	115	17	d.	d.	PROPN
ejpam-5711	115	18	a.	a.	PROPN
ejpam-5711	115	19	ali	ali	PROPN
ejpam-5711	115	20	,	,	PUNCT
ejpam-5711	115	21	g.	g.	PROPN
ejpam-5711	115	22	h.	h.	PROPN
ejpam-5711	116	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	116	2	/	/	SYM
ejpam-5711	116	3	eur	eur	PROPN
ejpam-5711	116	4	.	.	PUNCT
ejpam-5711	117	1	j.	j.	PROPN
ejpam-5711	117	2	pure	pure	PROPN
ejpam-5711	117	3	appl	appl	PROPN
ejpam-5711	117	4	.	.	PROPN
ejpam-5711	117	5	math	math	PROPN
ejpam-5711	117	6	,	,	PUNCT
ejpam-5711	117	7	18	18	NUM
ejpam-5711	117	8	(	(	PUNCT
ejpam-5711	117	9	1	1	NUM
ejpam-5711	117	10	)	)	PUNCT
ejpam-5711	117	11	(	(	PUNCT
ejpam-5711	117	12	2025	2025	NUM
ejpam-5711	117	13	)	)	PUNCT
ejpam-5711	117	14	,	,	PUNCT
ejpam-5711	117	15	5711	5711	NUM
ejpam-5711	117	16	6	6	NUM
ejpam-5711	117	17	of	of	ADP
ejpam-5711	117	18	15	15	NUM
ejpam-5711	117	19	dx(fgbn	dx(fgbn	NOUN
ejpam-5711	117	20	)	)	PUNCT
ejpam-5711	117	21	=	=	SYM
ejpam-5711	118	1	2[20(7n−2	2[20(7n−2	X
ejpam-5711	118	2	)	)	PUNCT
ejpam-5711	118	3	+	+	NUM
ejpam-5711	118	4	4]x2y2	4]x2y2	NUM
ejpam-5711	118	5	+	+	CCONJ
ejpam-5711	118	6	2[16(7n−2)−	2[16(7n−2)−	NUM
ejpam-5711	118	7	4]x2y4	4]x2y4	NUM
ejpam-5711	119	1	+	+	CCONJ
ejpam-5711	119	2	24(7n−2)x4y4	24(7n−2)x4y4	NUM
ejpam-5711	119	3	,	,	PUNCT
ejpam-5711	119	4	dy(fgbn	dy(fgbn	NOUN
ejpam-5711	119	5	)	)	PUNCT
ejpam-5711	119	6	=	=	PUNCT
ejpam-5711	120	1	2[20(7n−2	2[20(7n−2	NUM
ejpam-5711	120	2	)	)	PUNCT
ejpam-5711	120	3	+	+	CCONJ
ejpam-5711	120	4	4]x2y2	4]x2y2	NUM
ejpam-5711	120	5	+	+	CCONJ
ejpam-5711	120	6	4[16(7n−2)−	4[16(7n−2)−	NUM
ejpam-5711	120	7	4]x2y4	4]x2y4	NUM
ejpam-5711	121	1	+	+	CCONJ
ejpam-5711	121	2	24(7n−2)x4y4	24(7n−2)x4y4	NUM
ejpam-5711	121	3	,	,	PUNCT
ejpam-5711	121	4	dxdy(fgbn	dxdy(fgbn	PROPN
ejpam-5711	121	5	)	)	PUNCT
ejpam-5711	121	6	=	=	SYM
ejpam-5711	121	7	4[20(7n−2	4[20(7n−2	PROPN
ejpam-5711	121	8	)	)	PUNCT
ejpam-5711	122	1	+	+	CCONJ
ejpam-5711	122	2	4]x2y2	4]x2y2	NUM
ejpam-5711	123	1	+	+	CCONJ
ejpam-5711	123	2	8[16(7n−2)−	8[16(7n−2)−	ADJ
ejpam-5711	123	3	4]x2y4	4]x2y4	NUM
ejpam-5711	123	4	+	+	SYM
ejpam-5711	123	5	96(7n−2)x4y4	96(7n−2)x4y4	NUM
ejpam-5711	123	6	,	,	PUNCT
ejpam-5711	123	7	sx(fgbn	sx(fgbn	PROPN
ejpam-5711	123	8	)	)	PUNCT
ejpam-5711	123	9	=	=	PUNCT
ejpam-5711	124	1	[	[	X
ejpam-5711	124	2	10(7n−2	10(7n−2	NUM
ejpam-5711	124	3	)	)	PUNCT
ejpam-5711	125	1	+	+	NUM
ejpam-5711	125	2	2]x2y2	2]x2y2	NUM
ejpam-5711	125	3	+	+	CCONJ
ejpam-5711	125	4	[	[	X
ejpam-5711	125	5	8(7n−2)−	8(7n−2)−	NUM
ejpam-5711	125	6	2]x2y4	2]x2y4	NUM
ejpam-5711	125	7	+	+	CCONJ
ejpam-5711	125	8	3	3	NUM
ejpam-5711	125	9	2(7	2(7	NUM
ejpam-5711	125	10	n−2)x4y4	n−2)x4y4	ADJ
ejpam-5711	125	11	,	,	PUNCT
ejpam-5711	125	12	sy(fgbn	sy(fgbn	NOUN
ejpam-5711	125	13	)	)	PUNCT
ejpam-5711	125	14	=	=	PUNCT
ejpam-5711	126	1	[	[	X
ejpam-5711	126	2	10(7n−2	10(7n−2	NUM
ejpam-5711	126	3	)	)	PUNCT
ejpam-5711	127	1	+	+	NUM
ejpam-5711	127	2	2]x2y2	2]x2y2	NUM
ejpam-5711	127	3	+	+	PUNCT
ejpam-5711	128	1	[	[	X
ejpam-5711	128	2	4(7n−2)−	4(7n−2)−	NUM
ejpam-5711	128	3	1]x2y4	1]x2y4	NUM
ejpam-5711	128	4	+	+	CCONJ
ejpam-5711	128	5	3	3	NUM
ejpam-5711	128	6	2(7	2(7	NUM
ejpam-5711	128	7	n−2)x4y4	n−2)x4y4	ADJ
ejpam-5711	128	8	,	,	PUNCT
ejpam-5711	128	9	sxsy(fgbn	sxsy(fgbn	NOUN
ejpam-5711	128	10	)	)	PUNCT
ejpam-5711	128	11	=	=	PUNCT
ejpam-5711	129	1	[	[	X
ejpam-5711	129	2	5(7n−2	5(7n−2	NUM
ejpam-5711	129	3	)	)	PUNCT
ejpam-5711	130	1	+	+	CCONJ
ejpam-5711	131	1	1]x2y2	1]x2y2	NUM
ejpam-5711	131	2	+	+	SYM
ejpam-5711	131	3	1	1	NUM
ejpam-5711	131	4	2	2	NUM
ejpam-5711	131	5	[	[	SYM
ejpam-5711	131	6	4(7	4(7	NUM
ejpam-5711	131	7	n−2)−	n−2)−	VERB
ejpam-5711	131	8	1]x2y4	1]x2y4	NUM
ejpam-5711	131	9	+	+	CCONJ
ejpam-5711	131	10	3	3	NUM
ejpam-5711	131	11	8(7	8(7	NUM
ejpam-5711	131	12	n−2)x4y4	n−2)x4y4	NOUN
ejpam-5711	131	13	,	,	PUNCT
ejpam-5711	131	14	sxdy(fgbn	sxdy(fgbn	PROPN
ejpam-5711	131	15	)	)	PUNCT
ejpam-5711	132	1	=	=	PUNCT
ejpam-5711	133	1	[	[	X
ejpam-5711	133	2	20(7n−2	20(7n−2	NUM
ejpam-5711	133	3	)	)	PUNCT
ejpam-5711	134	1	+	+	CCONJ
ejpam-5711	134	2	4]x2y2	4]x2y2	NUM
ejpam-5711	134	3	+	+	CCONJ
ejpam-5711	134	4	2[16(7n−2)−	2[16(7n−2)−	NUM
ejpam-5711	134	5	4]x2y4	4]x2y4	NUM
ejpam-5711	134	6	+	+	CCONJ
ejpam-5711	134	7	6(7n−2)x4y4	6(7n−2)x4y4	NOUN
ejpam-5711	134	8	,	,	PUNCT
ejpam-5711	134	9	sydx(fgbn	sydx(fgbn	NOUN
ejpam-5711	134	10	)	)	PUNCT
ejpam-5711	135	1	=	=	PUNCT
ejpam-5711	136	1	[	[	X
ejpam-5711	136	2	20(7n−2	20(7n−2	NUM
ejpam-5711	136	3	)	)	PUNCT
ejpam-5711	137	1	+	+	CCONJ
ejpam-5711	137	2	4]x2y2	4]x2y2	NUM
ejpam-5711	138	1	+	+	CCONJ
ejpam-5711	138	2	1	1	NUM
ejpam-5711	138	3	2	2	NUM
ejpam-5711	138	4	[	[	X
ejpam-5711	138	5	16(7	16(7	NUM
ejpam-5711	138	6	n−2)−	n−2)−	VERB
ejpam-5711	138	7	4]x2y4	4]x2y4	NUM
ejpam-5711	138	8	+	+	CCONJ
ejpam-5711	138	9	6(7n−2)x4y4	6(7n−2)x4y4	NOUN
ejpam-5711	138	10	,	,	PUNCT
ejpam-5711	138	11	sxj(fgbn	sxj(fgbn	NOUN
ejpam-5711	138	12	)	)	PUNCT
ejpam-5711	138	13	=	=	PUNCT
ejpam-5711	139	1	[	[	X
ejpam-5711	139	2	5(7n−2	5(7n−2	NUM
ejpam-5711	139	3	)	)	PUNCT
ejpam-5711	139	4	+	+	CCONJ
ejpam-5711	140	1	1]x4	1]x4	NUM
ejpam-5711	140	2	+	+	CCONJ
ejpam-5711	140	3	2	2	NUM
ejpam-5711	140	4	3	3	NUM
ejpam-5711	140	5	[	[	X
ejpam-5711	140	6	4(7	4(7	NOUN
ejpam-5711	140	7	n−2)−	n−2)−	NOUN
ejpam-5711	140	8	1]x6	1]x6	NUM
ejpam-5711	140	9	+	+	CCONJ
ejpam-5711	140	10	3	3	NUM
ejpam-5711	140	11	4(7	4(7	NUM
ejpam-5711	140	12	n−2)x8	n−2)x8	NUM
ejpam-5711	140	13	,	,	PUNCT
ejpam-5711	140	14	sxj(dxdy(fgbn	sxj(dxdy(fgbn	NOUN
ejpam-5711	140	15	)	)	PUNCT
ejpam-5711	140	16	)	)	PUNCT
ejpam-5711	141	1	=	=	PUNCT
ejpam-5711	142	1	[	[	X
ejpam-5711	142	2	20(7n−2	20(7n−2	NUM
ejpam-5711	142	3	)	)	PUNCT
ejpam-5711	143	1	+	+	CCONJ
ejpam-5711	143	2	4]x4	4]x4	NUM
ejpam-5711	143	3	+	+	CCONJ
ejpam-5711	143	4	4	4	NUM
ejpam-5711	143	5	3	3	NUM
ejpam-5711	144	1	[	[	X
ejpam-5711	144	2	16(7	16(7	NUM
ejpam-5711	144	3	n−2)−	n−2)−	VERB
ejpam-5711	144	4	4]x6	4]x6	PROPN
ejpam-5711	144	5	+	+	CCONJ
ejpam-5711	144	6	12(7n−2)x8	12(7n−2)x8	PROPN
ejpam-5711	144	7	,	,	PUNCT
ejpam-5711	144	8	dγ	dγ	ADP
ejpam-5711	144	9	xd	xd	ADV
ejpam-5711	144	10	γ	γ	PROPN
ejpam-5711	144	11	y	y	PROPN
ejpam-5711	144	12	(	(	PUNCT
ejpam-5711	144	13	fgbn	fgbn	NOUN
ejpam-5711	144	14	)	)	PUNCT
ejpam-5711	144	15	=	=	SYM
ejpam-5711	145	1	22γ+2[5(7n−2	22γ+2[5(7n−2	X
ejpam-5711	145	2	)	)	PUNCT
ejpam-5711	146	1	+	+	CCONJ
ejpam-5711	147	1	1]x2y2	1]x2y2	NUM
ejpam-5711	147	2	+	+	CCONJ
ejpam-5711	147	3	23γ+2[4(7n−2)−	23γ+2[4(7n−2)−	NUM
ejpam-5711	147	4	1]x2y4	1]x2y4	NUM
ejpam-5711	147	5	+	+	CCONJ
ejpam-5711	147	6	3(24γ+1)(7n−2)x4y4	3(24γ+1)(7n−2)x4y4	NUM
ejpam-5711	147	7	.	.	PUNCT
ejpam-5711	148	1	thus	thus	ADV
ejpam-5711	148	2	,	,	PUNCT
ejpam-5711	148	3	(	(	PUNCT
ejpam-5711	148	4	i	i	NOUN
ejpam-5711	148	5	)	)	PUNCT
ejpam-5711	148	6	m1(fgbn	m1(fgbn	NOUN
ejpam-5711	148	7	)	)	PUNCT
ejpam-5711	148	8	=	=	PUNCT
ejpam-5711	148	9	(	(	PUNCT
ejpam-5711	148	10	dx	dx	PROPN
ejpam-5711	148	11	+	+	PROPN
ejpam-5711	148	12	dy)(m(fgbn;x	dy)(m(fgbn;x	PROPN
ejpam-5711	148	13	,	,	PUNCT
ejpam-5711	148	14	y))|x	y))|x	PROPN
ejpam-5711	148	15	=	=	SYM
ejpam-5711	148	16	y=1	y=1	NOUN
ejpam-5711	148	17	=	=	SYM
ejpam-5711	148	18	32(7n−1)−	32(7n−1)−	NUM
ejpam-5711	148	19	8	8	NUM
ejpam-5711	148	20	.	.	PUNCT
ejpam-5711	149	1	(	(	PUNCT
ejpam-5711	149	2	ii	ii	NOUN
ejpam-5711	149	3	)	)	PUNCT
ejpam-5711	149	4	m2(fgbn	m2(fgbn	NOUN
ejpam-5711	149	5	)	)	PUNCT
ejpam-5711	150	1	=	=	PRON
ejpam-5711	150	2	(	(	PUNCT
ejpam-5711	150	3	dxdy)(m(fgbn;x	dxdy)(m(fgbn;x	PROPN
ejpam-5711	150	4	,	,	PUNCT
ejpam-5711	150	5	y))|x	y))|x	PROPN
ejpam-5711	150	6	=	=	SYM
ejpam-5711	150	7	y=1	y=1	NOUN
ejpam-5711	150	8	=	=	SYM
ejpam-5711	151	1	304(7n−2)−	304(7n−2)−	NUM
ejpam-5711	151	2	16	16	NUM
ejpam-5711	151	3	.	.	PUNCT
ejpam-5711	152	1	(	(	PUNCT
ejpam-5711	152	2	iii	iii	NOUN
ejpam-5711	152	3	)	)	PUNCT
ejpam-5711	152	4	mm2(fgbn	mm2(fgbn	NOUN
ejpam-5711	152	5	)	)	PUNCT
ejpam-5711	153	1	=	=	SYM
ejpam-5711	153	2	(	(	PUNCT
ejpam-5711	153	3	sxsy)(m(fgbn;x	sxsy)(m(fgbn;x	NOUN
ejpam-5711	153	4	,	,	PUNCT
ejpam-5711	153	5	y))|x	y))|x	PROPN
ejpam-5711	153	6	=	=	SYM
ejpam-5711	153	7	y=1	y=1	NOUN
ejpam-5711	153	8	=	=	SYM
ejpam-5711	153	9	59	59	NUM
ejpam-5711	153	10	8	8	NUM
ejpam-5711	153	11	(	(	PUNCT
ejpam-5711	153	12	7	7	NUM
ejpam-5711	153	13	n−2	n−2	PROPN
ejpam-5711	153	14	)	)	PUNCT
ejpam-5711	153	15	+	+	CCONJ
ejpam-5711	153	16	1	1	NUM
ejpam-5711	153	17	2	2	NUM
ejpam-5711	153	18	.	.	PUNCT
ejpam-5711	154	1	(	(	PUNCT
ejpam-5711	154	2	iv	iv	X
ejpam-5711	154	3	)	)	PUNCT
ejpam-5711	154	4	rγ(fgbn	rγ(fgbn	PROPN
ejpam-5711	154	5	)	)	PUNCT
ejpam-5711	155	1	=	=	PRON
ejpam-5711	155	2	(	(	PUNCT
ejpam-5711	155	3	dγ	dγ	NOUN
ejpam-5711	155	4	xd	xd	INTJ
ejpam-5711	155	5	γ	γ	PROPN
ejpam-5711	155	6	y	y	PROPN
ejpam-5711	155	7	)	)	PUNCT
ejpam-5711	155	8	(	(	PUNCT
ejpam-5711	155	9	m(fgbn;x	m(fgbn;x	PROPN
ejpam-5711	155	10	,	,	PUNCT
ejpam-5711	155	11	y))|x	y))|x	PROPN
ejpam-5711	155	12	=	=	SYM
ejpam-5711	155	13	y=1	y=1	NOUN
ejpam-5711	155	14	=	=	PUNCT
ejpam-5711	156	1	[	[	X
ejpam-5711	156	2	5(22γ+2	5(22γ+2	NUM
ejpam-5711	156	3	)	)	PUNCT
ejpam-5711	157	1	+	+	NUM
ejpam-5711	157	2	23γ+4	23γ+4	NUM
ejpam-5711	157	3	+	+	CCONJ
ejpam-5711	157	4	3(24γ+1)](7n−2	3(24γ+1)](7n−2	NUM
ejpam-5711	157	5	)	)	PUNCT
ejpam-5711	157	6	+	+	NUM
ejpam-5711	157	7	22γ+2	22γ+2	NUM
ejpam-5711	157	8	−	−	PROPN
ejpam-5711	157	9	23γ+2	23γ+2	NUM
ejpam-5711	157	10	.	.	PUNCT
ejpam-5711	158	1	(	(	PUNCT
ejpam-5711	158	2	v	v	NOUN
ejpam-5711	158	3	)	)	PUNCT
ejpam-5711	158	4	ssd(fgbn	ssd(fgbn	NOUN
ejpam-5711	158	5	)	)	PUNCT
ejpam-5711	158	6	=	=	PUNCT
ejpam-5711	158	7	(	(	PUNCT
ejpam-5711	158	8	sydx	sydx	NOUN
ejpam-5711	158	9	+	+	CCONJ
ejpam-5711	158	10	sxdy)(m(fgbn;x	sxdy)(m(fgbn;x	PROPN
ejpam-5711	158	11	,	,	PUNCT
ejpam-5711	158	12	y))|x	y))|x	PROPN
ejpam-5711	158	13	=	=	SYM
ejpam-5711	158	14	y=1	y=1	NOUN
ejpam-5711	158	15	=	=	SYM
ejpam-5711	158	16	92(7n−2)−	92(7n−2)−	NUM
ejpam-5711	158	17	2	2	NUM
ejpam-5711	158	18	.	.	PUNCT
ejpam-5711	158	19	(	(	PUNCT
ejpam-5711	158	20	vi	vi	NOUN
ejpam-5711	158	21	)	)	PUNCT
ejpam-5711	158	22	h(fgbn	h(fgbn	NOUN
ejpam-5711	158	23	)	)	PUNCT
ejpam-5711	158	24	=	=	PUNCT
ejpam-5711	159	1	(	(	PUNCT
ejpam-5711	159	2	2sxj)(m(fgbn	2sxj)(m(fgbn	NUM
ejpam-5711	159	3	;	;	PUNCT
ejpam-5711	159	4	x	x	X
ejpam-5711	159	5	,	,	PUNCT
ejpam-5711	159	6	y))|x=1	y))|x=1	PROPN
ejpam-5711	159	7	=	=	NOUN
ejpam-5711	159	8	101	101	NUM
ejpam-5711	159	9	6	6	NUM
ejpam-5711	159	10	(	(	PUNCT
ejpam-5711	159	11	7n−2	7n−2	NUM
ejpam-5711	159	12	)	)	PUNCT
ejpam-5711	159	13	+	+	CCONJ
ejpam-5711	159	14	2	2	NUM
ejpam-5711	159	15	3	3	NUM
ejpam-5711	159	16	.	.	PUNCT
ejpam-5711	160	1	(	(	PUNCT
ejpam-5711	160	2	vii	vii	PROPN
ejpam-5711	160	3	)	)	PUNCT
ejpam-5711	160	4	i(fgbn	i(fgbn	NOUN
ejpam-5711	160	5	)	)	PUNCT
ejpam-5711	161	1	=	=	SYM
ejpam-5711	161	2	(	(	PUNCT
ejpam-5711	161	3	sxj)(dxdy(m(fgbn;x	sxj)(dxdy(m(fgbn;x	PROPN
ejpam-5711	161	4	,	,	PUNCT
ejpam-5711	161	5	y)))|x=1	y)))|x=1	X
ejpam-5711	161	6	=	=	NOUN
ejpam-5711	161	7	160	160	NUM
ejpam-5711	161	8	3	3	NUM
ejpam-5711	161	9	(	(	PUNCT
ejpam-5711	161	10	7n−2)−	7n−2)−	NUM
ejpam-5711	161	11	4	4	NUM
ejpam-5711	161	12	3	3	NUM
ejpam-5711	161	13	.	.	PUNCT
ejpam-5711	162	1	2.2	2.2	NUM
ejpam-5711	162	2	.	.	PUNCT
ejpam-5711	163	1	pythagoras	pythagoras	PROPN
ejpam-5711	163	2	tree	tree	PROPN
ejpam-5711	163	3	pythagoras	pythagoras	PROPN
ejpam-5711	163	4	tree	tree	PROPN
ejpam-5711	163	5	(	(	PUNCT
ejpam-5711	163	6	ptn	ptn	PROPN
ejpam-5711	163	7	)	)	PUNCT
ejpam-5711	163	8	,	,	PUNCT
ejpam-5711	163	9	n	n	PRON
ejpam-5711	163	10	≥	≥	NOUN
ejpam-5711	163	11	1	1	NUM
ejpam-5711	163	12	is	be	AUX
ejpam-5711	163	13	a	a	DET
ejpam-5711	163	14	fractal	fractal	NOUN
ejpam-5711	163	15	that	that	PRON
ejpam-5711	163	16	begins	begin	VERB
ejpam-5711	163	17	with	with	ADP
ejpam-5711	163	18	a	a	DET
ejpam-5711	163	19	square.it	square.it	PRON
ejpam-5711	163	20	involves	involve	VERB
ejpam-5711	163	21	creating	create	VERB
ejpam-5711	163	22	a	a	DET
ejpam-5711	163	23	right	right	ADJ
ejpam-5711	163	24	isosceles	isoscele	NOUN
ejpam-5711	163	25	triangle	triangle	VERB
ejpam-5711	163	26	with	with	ADP
ejpam-5711	163	27	its	its	PRON
ejpam-5711	163	28	hypotenuse	hypotenuse	NOUN
ejpam-5711	163	29	along	along	ADP
ejpam-5711	163	30	the	the	DET
ejpam-5711	163	31	top	top	ADJ
ejpam-5711	163	32	edge	edge	NOUN
ejpam-5711	163	33	of	of	ADP
ejpam-5711	163	34	the	the	DET
ejpam-5711	163	35	square	square	NOUN
ejpam-5711	163	36	.	.	PUNCT
ejpam-5711	164	1	squares	square	NOUN
ejpam-5711	164	2	are	be	AUX
ejpam-5711	164	3	then	then	ADV
ejpam-5711	164	4	constructed	construct	VERB
ejpam-5711	164	5	along	along	ADP
ejpam-5711	164	6	the	the	DET
ejpam-5711	164	7	other	other	ADJ
ejpam-5711	164	8	two	two	NUM
ejpam-5711	164	9	sides	side	NOUN
ejpam-5711	164	10	of	of	ADP
ejpam-5711	164	11	this	this	DET
ejpam-5711	164	12	triangle	triangle	NOUN
ejpam-5711	164	13	.	.	PUNCT
ejpam-5711	165	1	this	this	DET
ejpam-5711	165	2	process	process	NOUN
ejpam-5711	165	3	is	be	AUX
ejpam-5711	165	4	repeated	repeat	VERB
ejpam-5711	165	5	recursively	recursively	ADV
ejpam-5711	165	6	for	for	ADP
ejpam-5711	165	7	each	each	DET
ejpam-5711	165	8	new	new	ADJ
ejpam-5711	165	9	square	square	NOUN
ejpam-5711	165	10	created	create	VERB
ejpam-5711	165	11	.	.	PUNCT
ejpam-5711	166	1	see	see	VERB
ejpam-5711	166	2	figure	figure	NOUN
ejpam-5711	166	3	2	2	NUM
ejpam-5711	166	4	.	.	PUNCT
ejpam-5711	166	5	n.	n.	PROPN
ejpam-5711	166	6	t.	t.	PROPN
ejpam-5711	166	7	sarhan	sarhan	PROPN
ejpam-5711	166	8	,	,	PUNCT
ejpam-5711	166	9	d.	d.	PROPN
ejpam-5711	166	10	a.	a.	PROPN
ejpam-5711	166	11	ali	ali	PROPN
ejpam-5711	166	12	,	,	PUNCT
ejpam-5711	166	13	g.	g.	PROPN
ejpam-5711	166	14	h.	h.	PROPN
ejpam-5711	167	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	167	2	/	/	SYM
ejpam-5711	167	3	eur	eur	PROPN
ejpam-5711	167	4	.	.	PUNCT
ejpam-5711	168	1	j.	j.	PROPN
ejpam-5711	168	2	pure	pure	PROPN
ejpam-5711	168	3	appl	appl	PROPN
ejpam-5711	168	4	.	.	PROPN
ejpam-5711	168	5	math	math	PROPN
ejpam-5711	168	6	,	,	PUNCT
ejpam-5711	168	7	18	18	NUM
ejpam-5711	168	8	(	(	PUNCT
ejpam-5711	168	9	1	1	NUM
ejpam-5711	168	10	)	)	PUNCT
ejpam-5711	168	11	(	(	PUNCT
ejpam-5711	168	12	2025	2025	NUM
ejpam-5711	168	13	)	)	PUNCT
ejpam-5711	168	14	,	,	PUNCT
ejpam-5711	168	15	5711	5711	NUM
ejpam-5711	168	16	7	7	NUM
ejpam-5711	168	17	of	of	ADP
ejpam-5711	168	18	15	15	NUM
ejpam-5711	168	19	pt0	pt0	NOUN
ejpam-5711	168	20	pt1	pt1	PROPN
ejpam-5711	168	21	pt2	pt2	PROPN
ejpam-5711	168	22	pt8	pt8	PROPN
ejpam-5711	168	23	figure	figure	NOUN
ejpam-5711	168	24	2	2	NUM
ejpam-5711	168	25	:	:	PUNCT
ejpam-5711	168	26	pythagoras	pythagoras	PROPN
ejpam-5711	168	27	tree	tree	NOUN
ejpam-5711	168	28	pt0	pt0	PROPN
ejpam-5711	168	29	,	,	PUNCT
ejpam-5711	168	30	pt1	pt1	PROPN
ejpam-5711	168	31	,	,	PUNCT
ejpam-5711	168	32	pt2	pt2	PROPN
ejpam-5711	168	33	and	and	CCONJ
ejpam-5711	168	34	pt8	pt8	PROPN
ejpam-5711	168	35	.	.	PUNCT
ejpam-5711	169	1	in	in	ADP
ejpam-5711	169	2	the	the	DET
ejpam-5711	169	3	rest	rest	NOUN
ejpam-5711	169	4	of	of	ADP
ejpam-5711	169	5	this	this	DET
ejpam-5711	169	6	subsection	subsection	NOUN
ejpam-5711	169	7	,	,	PUNCT
ejpam-5711	169	8	we	we	PRON
ejpam-5711	169	9	determine	determine	VERB
ejpam-5711	169	10	the	the	DET
ejpam-5711	169	11	m	m	NOUN
ejpam-5711	169	12	-	-	NOUN
ejpam-5711	169	13	polynomial	polynomial	ADJ
ejpam-5711	169	14	of	of	ADP
ejpam-5711	169	15	the	the	DET
ejpam-5711	169	16	pythagoras	pythagoras	PROPN
ejpam-5711	169	17	tree	tree	NOUN
ejpam-5711	169	18	and	and	CCONJ
ejpam-5711	169	19	with	with	ADP
ejpam-5711	169	20	the	the	DET
ejpam-5711	169	21	help	help	NOUN
ejpam-5711	169	22	of	of	ADP
ejpam-5711	169	23	the	the	DET
ejpam-5711	169	24	m	m	NOUN
ejpam-5711	169	25	-	-	NOUN
ejpam-5711	169	26	polynomial	polynomial	ADJ
ejpam-5711	169	27	,	,	PUNCT
ejpam-5711	169	28	we	we	PRON
ejpam-5711	169	29	find	find	VERB
ejpam-5711	169	30	some	some	DET
ejpam-5711	169	31	degree	degree	NOUN
ejpam-5711	169	32	-	-	PUNCT
ejpam-5711	169	33	based	base	VERB
ejpam-5711	169	34	topological	topological	ADJ
ejpam-5711	169	35	indices.the	indices.the	DET
ejpam-5711	169	36	next	next	ADJ
ejpam-5711	169	37	theorem	theorem	NOUN
ejpam-5711	169	38	presents	present	VERB
ejpam-5711	169	39	the	the	DET
ejpam-5711	169	40	calculation	calculation	NOUN
ejpam-5711	169	41	of	of	ADP
ejpam-5711	169	42	the	the	DET
ejpam-5711	169	43	m	m	NOUN
ejpam-5711	169	44	-	-	NOUN
ejpam-5711	169	45	polynomial	polynomial	ADJ
ejpam-5711	169	46	for	for	ADP
ejpam-5711	169	47	the	the	DET
ejpam-5711	169	48	pythagoras	pythagoras	PROPN
ejpam-5711	169	49	tree	tree	PROPN
ejpam-5711	169	50	.	.	PUNCT
ejpam-5711	170	1	theorem	theorem	NOUN
ejpam-5711	170	2	2	2	NUM
ejpam-5711	170	3	.	.	PUNCT
ejpam-5711	171	1	let	let	VERB
ejpam-5711	171	2	ptn	ptn	PROPN
ejpam-5711	171	3	,	,	PUNCT
ejpam-5711	171	4	n	n	PRON
ejpam-5711	171	5	≥	≥	NOUN
ejpam-5711	171	6	1	1	NUM
ejpam-5711	171	7	be	be	AUX
ejpam-5711	171	8	the	the	DET
ejpam-5711	171	9	pythagoras	pythagoras	PROPN
ejpam-5711	171	10	tree	tree	NOUN
ejpam-5711	171	11	.	.	PUNCT
ejpam-5711	172	1	then	then	ADV
ejpam-5711	172	2	,	,	PUNCT
ejpam-5711	172	3	m(ptn;x	m(ptn;x	PROPN
ejpam-5711	172	4	,	,	PUNCT
ejpam-5711	172	5	y	y	PROPN
ejpam-5711	172	6	)	)	PUNCT
ejpam-5711	172	7	=	=	PUNCT
ejpam-5711	172	8	(	(	PUNCT
ejpam-5711	173	1	1	1	NUM
ejpam-5711	173	2	+	+	NOUN
ejpam-5711	173	3	2n)x2y2	2n)x2y2	NUM
ejpam-5711	173	4	+	+	SYM
ejpam-5711	173	5	(	(	PUNCT
ejpam-5711	173	6	2	2	NUM
ejpam-5711	173	7	+	+	NUM
ejpam-5711	173	8	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	173	9	+	+	CCONJ
ejpam-5711	173	10	(	(	PUNCT
ejpam-5711	173	11	5	5	NUM
ejpam-5711	173	12	·	·	SYM
ejpam-5711	173	13	2n	2n	NUM
ejpam-5711	173	14	−	−	PROPN
ejpam-5711	173	15	7)x4y4	7)x4y4	NOUN
ejpam-5711	173	16	.	.	PUNCT
ejpam-5711	174	1	proof	proof	NOUN
ejpam-5711	174	2	.	.	PUNCT
ejpam-5711	175	1	let	let	VERB
ejpam-5711	175	2	ptn	ptn	PROPN
ejpam-5711	175	3	,	,	PUNCT
ejpam-5711	175	4	n	n	PRON
ejpam-5711	175	5	≥	≥	NOUN
ejpam-5711	175	6	1	1	NUM
ejpam-5711	175	7	be	be	AUX
ejpam-5711	175	8	the	the	DET
ejpam-5711	175	9	pythagoras	pythagoras	PROPN
ejpam-5711	175	10	tree	tree	NOUN
ejpam-5711	175	11	as	as	SCONJ
ejpam-5711	175	12	shown	show	VERB
ejpam-5711	175	13	in	in	ADP
ejpam-5711	175	14	figure	figure	NOUN
ejpam-5711	175	15	2	2	NUM
ejpam-5711	175	16	.	.	PUNCT
ejpam-5711	176	1	then	then	ADV
ejpam-5711	176	2	,	,	PUNCT
ejpam-5711	176	3	|v(ptn)|	|v(ptn)|	ADP
ejpam-5711	176	4	=	=	SYM
ejpam-5711	176	5	5	5	NUM
ejpam-5711	176	6	·	·	SYM
ejpam-5711	176	7	2n	2n	NUM
ejpam-5711	177	1	−	−	ADP
ejpam-5711	177	2	1	1	NUM
ejpam-5711	177	3	and	and	CCONJ
ejpam-5711	177	4	|e(ptn)|	|e(ptn)|	NOUN
ejpam-5711	177	5	=	=	SYM
ejpam-5711	177	6	(	(	PUNCT
ejpam-5711	177	7	2n+3	2n+3	NOUN
ejpam-5711	177	8	−	−	NOUN
ejpam-5711	177	9	4	4	NUM
ejpam-5711	177	10	)	)	PUNCT
ejpam-5711	177	11	.	.	PUNCT
ejpam-5711	178	1	the	the	DET
ejpam-5711	178	2	edge	edge	NOUN
ejpam-5711	178	3	set	set	VERB
ejpam-5711	178	4	e(ptn	e(ptn	PROPN
ejpam-5711	178	5	)	)	PUNCT
ejpam-5711	178	6	can	can	AUX
ejpam-5711	178	7	be	be	AUX
ejpam-5711	178	8	divided	divide	VERB
ejpam-5711	178	9	into	into	ADP
ejpam-5711	178	10	the	the	DET
ejpam-5711	178	11	following	follow	VERB
ejpam-5711	178	12	three	three	NUM
ejpam-5711	178	13	parts	part	NOUN
ejpam-5711	178	14	:	:	PUNCT
ejpam-5711	178	15	|e(2	|e(2	NOUN
ejpam-5711	178	16	,	,	PUNCT
ejpam-5711	178	17	2)|	2)|	NUM
ejpam-5711	178	18	=	=	SYM
ejpam-5711	178	19	|e	|e	NOUN
ejpam-5711	178	20	=	=	PUNCT
ejpam-5711	178	21	uv	uv	PROPN
ejpam-5711	178	22	∈	∈	PROPN
ejpam-5711	178	23	e(ptn	e(ptn	PROPN
ejpam-5711	178	24	)	)	PUNCT
ejpam-5711	178	25	:	:	PUNCT
ejpam-5711	178	26	du	du	PROPN
ejpam-5711	178	27	=	=	SYM
ejpam-5711	178	28	2	2	NUM
ejpam-5711	178	29	and	and	CCONJ
ejpam-5711	178	30	dv	dv	PROPN
ejpam-5711	179	1	=	=	PROPN
ejpam-5711	179	2	2|	2|	NUM
ejpam-5711	179	3	=	=	SYM
ejpam-5711	179	4	1	1	NUM
ejpam-5711	179	5	+	+	NUM
ejpam-5711	179	6	2n	2n	NUM
ejpam-5711	179	7	,	,	PUNCT
ejpam-5711	179	8	|e(2	|e(2	NOUN
ejpam-5711	179	9	,	,	PUNCT
ejpam-5711	179	10	4)|	4)|	NUM
ejpam-5711	179	11	=	=	SYM
ejpam-5711	179	12	|e	|e	NOUN
ejpam-5711	180	1	=	=	PUNCT
ejpam-5711	180	2	uv	uv	PROPN
ejpam-5711	180	3	∈	∈	PROPN
ejpam-5711	180	4	e(ptn	e(ptn	PROPN
ejpam-5711	180	5	)	)	PUNCT
ejpam-5711	180	6	:	:	PUNCT
ejpam-5711	180	7	du	du	PROPN
ejpam-5711	180	8	=	=	SYM
ejpam-5711	180	9	2	2	NUM
ejpam-5711	180	10	and	and	CCONJ
ejpam-5711	180	11	dv	dv	PROPN
ejpam-5711	180	12	=	=	PROPN
ejpam-5711	180	13	4|	4|	NUM
ejpam-5711	181	1	=	=	SYM
ejpam-5711	181	2	2	2	NUM
ejpam-5711	181	3	+	+	NUM
ejpam-5711	181	4	2n+1	2n+1	NOUN
ejpam-5711	181	5	,	,	PUNCT
ejpam-5711	181	6	and	and	CCONJ
ejpam-5711	181	7	|e(4	|e(4	NOUN
ejpam-5711	181	8	,	,	PUNCT
ejpam-5711	181	9	4)|	4)|	NUM
ejpam-5711	181	10	=	=	SYM
ejpam-5711	181	11	|e	|e	NOUN
ejpam-5711	181	12	=	=	PUNCT
ejpam-5711	181	13	uv	uv	PROPN
ejpam-5711	181	14	∈	∈	PROPN
ejpam-5711	181	15	e(ptn	e(ptn	PROPN
ejpam-5711	181	16	)	)	PUNCT
ejpam-5711	181	17	:	:	PUNCT
ejpam-5711	182	1	du	du	PROPN
ejpam-5711	182	2	=	=	SYM
ejpam-5711	182	3	4	4	NUM
ejpam-5711	182	4	and	and	CCONJ
ejpam-5711	182	5	dv	dv	PROPN
ejpam-5711	182	6	=	=	SYM
ejpam-5711	182	7	4|	4|	NUM
ejpam-5711	182	8	=	=	SYM
ejpam-5711	182	9	5	5	NUM
ejpam-5711	182	10	·	·	SYM
ejpam-5711	182	11	2n	2n	NUM
ejpam-5711	182	12	−	−	NOUN
ejpam-5711	182	13	7	7	NUM
ejpam-5711	182	14	.	.	PUNCT
ejpam-5711	183	1	thus	thus	ADV
ejpam-5711	183	2	,	,	PUNCT
ejpam-5711	183	3	the	the	DET
ejpam-5711	183	4	m	m	NOUN
ejpam-5711	183	5	-	-	ADJ
ejpam-5711	183	6	polynomial	polynomial	ADJ
ejpam-5711	183	7	of	of	ADP
ejpam-5711	183	8	ptn	ptn	PROPN
ejpam-5711	183	9	is	be	AUX
ejpam-5711	183	10	given	give	VERB
ejpam-5711	183	11	as	as	ADP
ejpam-5711	183	12	:	:	PUNCT
ejpam-5711	183	13	m(ptn;x	m(ptn;x	PROPN
ejpam-5711	183	14	,	,	PUNCT
ejpam-5711	183	15	y	y	PROPN
ejpam-5711	183	16	)	)	PUNCT
ejpam-5711	183	17	=	=	PUNCT
ejpam-5711	183	18	∑	∑	PUNCT
ejpam-5711	183	19	δ≤α≤β≤∆	δ≤α≤β≤∆	PROPN
ejpam-5711	183	20	mα	mα	PROPN
ejpam-5711	183	21	,	,	PUNCT
ejpam-5711	183	22	βx	βx	AUX
ejpam-5711	183	23	αyβ	αyβ	VERB
ejpam-5711	183	24	=	=	PUNCT
ejpam-5711	183	25	∑	∑	PUNCT
ejpam-5711	183	26	2≤2	2≤2	NUM
ejpam-5711	183	27	m2,2x	m2,2x	NOUN
ejpam-5711	183	28	2y2	2y2	NUM
ejpam-5711	183	29	+	+	CCONJ
ejpam-5711	183	30	∑	∑	PUNCT
ejpam-5711	183	31	2≤4	2≤4	SYM
ejpam-5711	183	32	m2,4x	m2,4x	PROPN
ejpam-5711	183	33	2y4	2y4	NUM
ejpam-5711	184	1	+	+	CCONJ
ejpam-5711	184	2	∑	∑	PUNCT
ejpam-5711	184	3	4≤4	4≤4	NUM
ejpam-5711	184	4	m4,4x	m4,4x	PROPN
ejpam-5711	184	5	4y4	4y4	NUM
ejpam-5711	185	1	=	=	SYM
ejpam-5711	185	2	|e(2	|e(2	NOUN
ejpam-5711	185	3	,	,	PUNCT
ejpam-5711	185	4	2)|x2y2	2)|x2y2	NUM
ejpam-5711	185	5	+	+	CCONJ
ejpam-5711	185	6	|e(2	|e(2	ADJ
ejpam-5711	185	7	,	,	PUNCT
ejpam-5711	185	8	4)|x2y4	4)|x2y4	NUM
ejpam-5711	185	9	+	+	CCONJ
ejpam-5711	185	10	|e(4	|e(4	NOUN
ejpam-5711	185	11	,	,	PUNCT
ejpam-5711	185	12	4)|x4y4	4)|x4y4	NOUN
ejpam-5711	185	13	=	=	SYM
ejpam-5711	185	14	(	(	PUNCT
ejpam-5711	185	15	1	1	NUM
ejpam-5711	185	16	+	+	SYM
ejpam-5711	185	17	2n)x2y2	2n)x2y2	NUM
ejpam-5711	185	18	+	+	CCONJ
ejpam-5711	185	19	(	(	PUNCT
ejpam-5711	185	20	2	2	NUM
ejpam-5711	185	21	+	+	NUM
ejpam-5711	185	22	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	185	23	+	+	CCONJ
ejpam-5711	185	24	(	(	PUNCT
ejpam-5711	185	25	5	5	NUM
ejpam-5711	185	26	·	·	SYM
ejpam-5711	185	27	2n	2n	NUM
ejpam-5711	185	28	−	−	PROPN
ejpam-5711	185	29	7)x4y4	7)x4y4	NOUN
ejpam-5711	185	30	.	.	PUNCT
ejpam-5711	186	1	now	now	ADV
ejpam-5711	186	2	,	,	PUNCT
ejpam-5711	186	3	we	we	PRON
ejpam-5711	186	4	provide	provide	VERB
ejpam-5711	186	5	several	several	ADJ
ejpam-5711	186	6	topological	topological	ADJ
ejpam-5711	186	7	indices	index	NOUN
ejpam-5711	186	8	based	base	VERB
ejpam-5711	186	9	on	on	ADP
ejpam-5711	186	10	degrees	degree	NOUN
ejpam-5711	186	11	using	use	VERB
ejpam-5711	186	12	the	the	DET
ejpam-5711	186	13	m	m	NOUN
ejpam-5711	186	14	-	-	ADJ
ejpam-5711	186	15	polynomial	polynomial	ADJ
ejpam-5711	186	16	of	of	ADP
ejpam-5711	186	17	the	the	DET
ejpam-5711	186	18	pythagoras	pythagoras	PROPN
ejpam-5711	186	19	tree	tree	NOUN
ejpam-5711	186	20	.	.	PUNCT
ejpam-5711	187	1	proposition	proposition	NOUN
ejpam-5711	187	2	2	2	NUM
ejpam-5711	187	3	.	.	PUNCT
ejpam-5711	188	1	let	let	VERB
ejpam-5711	188	2	ptn	ptn	PROPN
ejpam-5711	188	3	,	,	PUNCT
ejpam-5711	188	4	n	n	PRON
ejpam-5711	188	5	≥	≥	NOUN
ejpam-5711	188	6	1	1	NUM
ejpam-5711	188	7	be	be	AUX
ejpam-5711	188	8	the	the	DET
ejpam-5711	188	9	pythagoras	pythagoras	PROPN
ejpam-5711	188	10	tree	tree	NOUN
ejpam-5711	188	11	.	.	PUNCT
ejpam-5711	189	1	then	then	ADV
ejpam-5711	189	2	,	,	PUNCT
ejpam-5711	189	3	n.	n.	PROPN
ejpam-5711	189	4	t.	t.	PROPN
ejpam-5711	189	5	sarhan	sarhan	PROPN
ejpam-5711	189	6	,	,	PUNCT
ejpam-5711	189	7	d.	d.	PROPN
ejpam-5711	189	8	a.	a.	PROPN
ejpam-5711	189	9	ali	ali	PROPN
ejpam-5711	189	10	,	,	PUNCT
ejpam-5711	189	11	g.	g.	PROPN
ejpam-5711	189	12	h.	h.	PROPN
ejpam-5711	190	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	190	2	/	/	SYM
ejpam-5711	190	3	eur	eur	PROPN
ejpam-5711	190	4	.	.	PUNCT
ejpam-5711	191	1	j.	j.	PROPN
ejpam-5711	191	2	pure	pure	PROPN
ejpam-5711	191	3	appl	appl	PROPN
ejpam-5711	191	4	.	.	PROPN
ejpam-5711	191	5	math	math	PROPN
ejpam-5711	191	6	,	,	PUNCT
ejpam-5711	191	7	18	18	NUM
ejpam-5711	191	8	(	(	PUNCT
ejpam-5711	191	9	1	1	NUM
ejpam-5711	191	10	)	)	PUNCT
ejpam-5711	191	11	(	(	PUNCT
ejpam-5711	191	12	2025	2025	NUM
ejpam-5711	191	13	)	)	PUNCT
ejpam-5711	191	14	,	,	PUNCT
ejpam-5711	191	15	5711	5711	NUM
ejpam-5711	191	16	8	8	NUM
ejpam-5711	191	17	of	of	ADP
ejpam-5711	191	18	15	15	NUM
ejpam-5711	191	19	(	(	PUNCT
ejpam-5711	191	20	i	i	NOUN
ejpam-5711	191	21	)	)	PUNCT
ejpam-5711	191	22	m1(ptn	m1(ptn	PROPN
ejpam-5711	191	23	)	)	PUNCT
ejpam-5711	191	24	=	=	SYM
ejpam-5711	191	25	56	56	NUM
ejpam-5711	191	26	·	·	SYM
ejpam-5711	191	27	2n	2n	NUM
ejpam-5711	192	1	−	−	NUM
ejpam-5711	192	2	40	40	NUM
ejpam-5711	192	3	.	.	PUNCT
ejpam-5711	193	1	(	(	PUNCT
ejpam-5711	193	2	ii	ii	NOUN
ejpam-5711	193	3	)	)	PUNCT
ejpam-5711	193	4	m2(ptn	m2(ptn	PROPN
ejpam-5711	193	5	)	)	PUNCT
ejpam-5711	193	6	=	=	SYM
ejpam-5711	193	7	100	100	NUM
ejpam-5711	193	8	·	·	PUNCT
ejpam-5711	193	9	2n	2n	NUM
ejpam-5711	194	1	−	−	ADP
ejpam-5711	194	2	92	92	NUM
ejpam-5711	194	3	.	.	PUNCT
ejpam-5711	195	1	(	(	PUNCT
ejpam-5711	195	2	iii	iii	X
ejpam-5711	195	3	)	)	PUNCT
ejpam-5711	195	4	mm2(ptn	mm2(ptn	PROPN
ejpam-5711	195	5	)	)	PUNCT
ejpam-5711	195	6	=	=	SYM
ejpam-5711	195	7	13	13	NUM
ejpam-5711	195	8	16	16	NUM
ejpam-5711	195	9	·	·	SYM
ejpam-5711	195	10	2n	2n	NUM
ejpam-5711	196	1	+	+	CCONJ
ejpam-5711	196	2	1	1	NUM
ejpam-5711	196	3	16	16	NUM
ejpam-5711	196	4	.	.	PUNCT
ejpam-5711	197	1	(	(	PUNCT
ejpam-5711	197	2	iv	iv	X
ejpam-5711	197	3	)	)	PUNCT
ejpam-5711	197	4	rγ(ptn	rγ(ptn	PROPN
ejpam-5711	197	5	)	)	PUNCT
ejpam-5711	198	1	=	=	PUNCT
ejpam-5711	199	1	(	(	PUNCT
ejpam-5711	199	2	1	1	NUM
ejpam-5711	199	3	+	+	X
ejpam-5711	199	4	2γ+1	2γ+1	NUM
ejpam-5711	199	5	−	−	NUM
ejpam-5711	199	6	7	7	NUM
ejpam-5711	199	7	·	·	PUNCT
ejpam-5711	199	8	22γ)22γ	22γ)22γ	PROPN
ejpam-5711	200	1	+	+	CCONJ
ejpam-5711	200	2	(	(	PUNCT
ejpam-5711	200	3	1	1	NUM
ejpam-5711	200	4	+	+	CCONJ
ejpam-5711	200	5	2γ+1	2γ+1	NUM
ejpam-5711	200	6	+	+	CCONJ
ejpam-5711	200	7	5	5	NUM
ejpam-5711	200	8	·	·	SYM
ejpam-5711	200	9	22γ)22γ+n	22γ)22γ+n	NUM
ejpam-5711	200	10	.	.	PUNCT
ejpam-5711	201	1	(	(	PUNCT
ejpam-5711	201	2	v	v	NOUN
ejpam-5711	201	3	)	)	PUNCT
ejpam-5711	201	4	ssd(ptn	ssd(ptn	NOUN
ejpam-5711	201	5	)	)	PUNCT
ejpam-5711	202	1	=	=	SYM
ejpam-5711	202	2	17	17	NUM
ejpam-5711	202	3	·	·	SYM
ejpam-5711	202	4	2n	2n	NUM
ejpam-5711	202	5	−	−	NOUN
ejpam-5711	202	6	7	7	X
ejpam-5711	202	7	.	.	PUNCT
ejpam-5711	202	8	(	(	PUNCT
ejpam-5711	202	9	vi	vi	NOUN
ejpam-5711	202	10	)	)	PUNCT
ejpam-5711	202	11	h(ptn	h(ptn	NOUN
ejpam-5711	202	12	)	)	PUNCT
ejpam-5711	202	13	=	=	SYM
ejpam-5711	203	1	29	29	NUM
ejpam-5711	203	2	12(2	12(2	NUM
ejpam-5711	203	3	n)−	n)−	PROPN
ejpam-5711	203	4	7	7	NUM
ejpam-5711	203	5	12	12	NUM
ejpam-5711	203	6	.	.	PUNCT
ejpam-5711	204	1	(	(	PUNCT
ejpam-5711	204	2	vii	vii	PROPN
ejpam-5711	204	3	)	)	PUNCT
ejpam-5711	204	4	i(ptn	i(ptn	PROPN
ejpam-5711	204	5	)	)	PUNCT
ejpam-5711	204	6	=	=	SYM
ejpam-5711	205	1	41	41	NUM
ejpam-5711	205	2	3	3	NUM
ejpam-5711	205	3	2	2	NUM
ejpam-5711	205	4	n	n	NUM
ejpam-5711	205	5	−	−	PROPN
ejpam-5711	205	6	31	31	NUM
ejpam-5711	205	7	3	3	NUM
ejpam-5711	205	8	.	.	PUNCT
ejpam-5711	206	1	proof	proof	NOUN
ejpam-5711	206	2	.	.	PUNCT
ejpam-5711	207	1	since	since	SCONJ
ejpam-5711	207	2	,	,	PUNCT
ejpam-5711	207	3	m(ptn;x	m(ptn;x	PROPN
ejpam-5711	207	4	,	,	PUNCT
ejpam-5711	207	5	y	y	PROPN
ejpam-5711	207	6	)	)	PUNCT
ejpam-5711	207	7	=	=	PUNCT
ejpam-5711	207	8	(	(	PUNCT
ejpam-5711	207	9	1	1	NUM
ejpam-5711	207	10	+	+	SYM
ejpam-5711	207	11	2n)x2y2	2n)x2y2	NUM
ejpam-5711	207	12	+	+	CCONJ
ejpam-5711	207	13	(	(	PUNCT
ejpam-5711	207	14	2	2	NUM
ejpam-5711	207	15	+	+	NUM
ejpam-5711	207	16	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	207	17	+	+	CCONJ
ejpam-5711	207	18	(	(	PUNCT
ejpam-5711	207	19	5	5	NUM
ejpam-5711	207	20	·	·	SYM
ejpam-5711	207	21	2n	2n	NUM
ejpam-5711	207	22	−	−	PROPN
ejpam-5711	207	23	7)x4y4	7)x4y4	NOUN
ejpam-5711	207	24	.	.	PUNCT
ejpam-5711	208	1	then	then	ADV
ejpam-5711	208	2	,	,	PUNCT
ejpam-5711	208	3	we	we	PRON
ejpam-5711	208	4	have	have	VERB
ejpam-5711	208	5	dx(ptn	dx(ptn	NOUN
ejpam-5711	208	6	)	)	PUNCT
ejpam-5711	208	7	=	=	SYM
ejpam-5711	209	1	2(1	2(1	NUM
ejpam-5711	209	2	+	+	CCONJ
ejpam-5711	209	3	2n)x2y2	2n)x2y2	NUM
ejpam-5711	209	4	+	+	CCONJ
ejpam-5711	209	5	2(2	2(2	NUM
ejpam-5711	210	1	+	+	SYM
ejpam-5711	210	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	210	3	+	+	CCONJ
ejpam-5711	210	4	4(5	4(5	NUM
ejpam-5711	210	5	·	·	SYM
ejpam-5711	210	6	2n	2n	NUM
ejpam-5711	211	1	−	−	PROPN
ejpam-5711	211	2	7)x4y4	7)x4y4	NOUN
ejpam-5711	211	3	,	,	PUNCT
ejpam-5711	211	4	dy(ptn	dy(ptn	NOUN
ejpam-5711	211	5	)	)	PUNCT
ejpam-5711	211	6	=	=	SYM
ejpam-5711	211	7	2(1	2(1	NUM
ejpam-5711	212	1	+	+	CCONJ
ejpam-5711	212	2	2n)x2y2	2n)x2y2	NUM
ejpam-5711	212	3	+	+	CCONJ
ejpam-5711	212	4	4(2	4(2	NUM
ejpam-5711	213	1	+	+	CCONJ
ejpam-5711	213	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	213	3	+	+	CCONJ
ejpam-5711	213	4	4(5	4(5	NUM
ejpam-5711	213	5	·	·	SYM
ejpam-5711	213	6	2n	2n	NUM
ejpam-5711	214	1	−	−	PROPN
ejpam-5711	214	2	7)x4y4	7)x4y4	NOUN
ejpam-5711	214	3	,	,	PUNCT
ejpam-5711	214	4	dxdy(ptn	dxdy(ptn	NOUN
ejpam-5711	214	5	)	)	PUNCT
ejpam-5711	214	6	=	=	SYM
ejpam-5711	214	7	4(1	4(1	NOUN
ejpam-5711	215	1	+	+	CCONJ
ejpam-5711	216	1	2n)x2y2	2n)x2y2	NUM
ejpam-5711	216	2	+	+	CCONJ
ejpam-5711	216	3	8(2	8(2	NUM
ejpam-5711	217	1	+	+	CCONJ
ejpam-5711	217	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	217	3	+	+	CCONJ
ejpam-5711	217	4	16(5	16(5	NUM
ejpam-5711	217	5	·	·	PUNCT
ejpam-5711	217	6	2n	2n	NUM
ejpam-5711	217	7	−	−	PROPN
ejpam-5711	217	8	7)x4y4	7)x4y4	NOUN
ejpam-5711	217	9	,	,	PUNCT
ejpam-5711	217	10	d3	d3	PROPN
ejpam-5711	217	11	xd	xd	ADV
ejpam-5711	217	12	3	3	NUM
ejpam-5711	217	13	y(ptn	y(ptn	NOUN
ejpam-5711	217	14	)	)	PUNCT
ejpam-5711	217	15	=	=	PUNCT
ejpam-5711	218	1	64(1	64(1	NUM
ejpam-5711	218	2	+	+	CCONJ
ejpam-5711	218	3	2n)x2y2	2n)x2y2	NUM
ejpam-5711	218	4	+	+	SYM
ejpam-5711	218	5	512(2	512(2	NUM
ejpam-5711	218	6	+	+	NUM
ejpam-5711	218	7	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	219	1	+	+	SYM
ejpam-5711	219	2	4096(5	4096(5	PROPN
ejpam-5711	219	3	·	·	PUNCT
ejpam-5711	219	4	2n	2n	NUM
ejpam-5711	219	5	−	−	PROPN
ejpam-5711	219	6	7)x4y4	7)x4y4	NOUN
ejpam-5711	219	7	,	,	PUNCT
ejpam-5711	219	8	sx(ptn	sx(ptn	NOUN
ejpam-5711	219	9	)	)	PUNCT
ejpam-5711	219	10	=	=	SYM
ejpam-5711	219	11	1	1	NUM
ejpam-5711	219	12	2(1	2(1	NUM
ejpam-5711	219	13	+	+	CCONJ
ejpam-5711	219	14	2n)x2y2	2n)x2y2	NUM
ejpam-5711	219	15	+	+	CCONJ
ejpam-5711	219	16	1	1	NUM
ejpam-5711	219	17	2(2	2(2	NUM
ejpam-5711	220	1	+	+	CCONJ
ejpam-5711	220	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	220	3	+	+	SYM
ejpam-5711	220	4	1	1	NUM
ejpam-5711	220	5	4(5	4(5	NUM
ejpam-5711	220	6	·	·	SYM
ejpam-5711	220	7	2	2	NUM
ejpam-5711	220	8	n	n	NUM
ejpam-5711	220	9	−	−	PROPN
ejpam-5711	220	10	7)x4y4	7)x4y4	NOUN
ejpam-5711	220	11	,	,	PUNCT
ejpam-5711	220	12	sy(ptn	sy(ptn	PROPN
ejpam-5711	220	13	)	)	PUNCT
ejpam-5711	220	14	=	=	SYM
ejpam-5711	221	1	1	1	NUM
ejpam-5711	221	2	2(1	2(1	NUM
ejpam-5711	221	3	+	+	CCONJ
ejpam-5711	221	4	2n)x2y2	2n)x2y2	NUM
ejpam-5711	221	5	+	+	CCONJ
ejpam-5711	221	6	1	1	NUM
ejpam-5711	221	7	4(2	4(2	NUM
ejpam-5711	222	1	+	+	CCONJ
ejpam-5711	222	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	222	3	+	+	SYM
ejpam-5711	222	4	1	1	NUM
ejpam-5711	222	5	4(5	4(5	NUM
ejpam-5711	222	6	·	·	SYM
ejpam-5711	222	7	2	2	NUM
ejpam-5711	222	8	n	n	NUM
ejpam-5711	222	9	−	−	PROPN
ejpam-5711	222	10	7)x4y4	7)x4y4	NOUN
ejpam-5711	222	11	,	,	PUNCT
ejpam-5711	222	12	sxsy(ptn	sxsy(ptn	NOUN
ejpam-5711	222	13	)	)	PUNCT
ejpam-5711	222	14	=	=	SYM
ejpam-5711	222	15	1	1	NUM
ejpam-5711	222	16	4(1	4(1	NUM
ejpam-5711	222	17	+	+	CCONJ
ejpam-5711	222	18	2n)x2y2	2n)x2y2	NUM
ejpam-5711	222	19	+	+	CCONJ
ejpam-5711	222	20	1	1	NUM
ejpam-5711	222	21	8(2	8(2	NUM
ejpam-5711	223	1	+	+	NUM
ejpam-5711	223	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	223	3	+	+	CCONJ
ejpam-5711	223	4	1	1	NUM
ejpam-5711	223	5	16(5	16(5	NUM
ejpam-5711	223	6	·	·	SYM
ejpam-5711	223	7	2	2	NUM
ejpam-5711	223	8	n	n	NUM
ejpam-5711	223	9	−	−	PROPN
ejpam-5711	223	10	7)x4y4	7)x4y4	NOUN
ejpam-5711	223	11	,	,	PUNCT
ejpam-5711	223	12	sxdy(ptn	sxdy(ptn	NOUN
ejpam-5711	223	13	)	)	PUNCT
ejpam-5711	223	14	=	=	PUNCT
ejpam-5711	224	1	(	(	PUNCT
ejpam-5711	224	2	1	1	NUM
ejpam-5711	224	3	+	+	SYM
ejpam-5711	224	4	2n)x2y2	2n)x2y2	NUM
ejpam-5711	224	5	+	+	CCONJ
ejpam-5711	224	6	2(2	2(2	NUM
ejpam-5711	225	1	+	+	CCONJ
ejpam-5711	225	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	225	3	+	+	CCONJ
ejpam-5711	225	4	(	(	PUNCT
ejpam-5711	225	5	5	5	NUM
ejpam-5711	225	6	·	·	SYM
ejpam-5711	225	7	2n	2n	NUM
ejpam-5711	225	8	−	−	PROPN
ejpam-5711	225	9	7)x4y4	7)x4y4	NOUN
ejpam-5711	225	10	,	,	PUNCT
ejpam-5711	225	11	sydx(ptn	sydx(ptn	NOUN
ejpam-5711	225	12	)	)	PUNCT
ejpam-5711	225	13	=	=	PUNCT
ejpam-5711	226	1	(	(	PUNCT
ejpam-5711	226	2	1	1	NUM
ejpam-5711	226	3	+	+	SYM
ejpam-5711	226	4	2n)x2y2	2n)x2y2	NUM
ejpam-5711	226	5	+	+	CCONJ
ejpam-5711	226	6	1	1	NUM
ejpam-5711	226	7	2(2	2(2	NUM
ejpam-5711	227	1	+	+	CCONJ
ejpam-5711	227	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	227	3	+	+	CCONJ
ejpam-5711	227	4	(	(	PUNCT
ejpam-5711	227	5	5	5	NUM
ejpam-5711	227	6	·	·	SYM
ejpam-5711	227	7	2n	2n	NUM
ejpam-5711	227	8	−	−	PROPN
ejpam-5711	227	9	7)x4y4	7)x4y4	NOUN
ejpam-5711	227	10	,	,	PUNCT
ejpam-5711	227	11	sxj(ptn	sxj(ptn	NOUN
ejpam-5711	227	12	)	)	PUNCT
ejpam-5711	228	1	=	=	SYM
ejpam-5711	228	2	i	i	PRON
ejpam-5711	228	3	4(1	4(1	NUM
ejpam-5711	229	1	+	+	CCONJ
ejpam-5711	230	1	2n)x4	2n)x4	NUM
ejpam-5711	230	2	+	+	CCONJ
ejpam-5711	230	3	1	1	NUM
ejpam-5711	230	4	6(2	6(2	NUM
ejpam-5711	230	5	+	+	CCONJ
ejpam-5711	230	6	2n+1)x6	2n+1)x6	NUM
ejpam-5711	230	7	+	+	CCONJ
ejpam-5711	230	8	1	1	NUM
ejpam-5711	230	9	8(5	8(5	NUM
ejpam-5711	230	10	·	·	SYM
ejpam-5711	230	11	2	2	NUM
ejpam-5711	230	12	n	n	NUM
ejpam-5711	230	13	−	−	PROPN
ejpam-5711	230	14	7)x8	7)x8	NUM
ejpam-5711	230	15	,	,	PUNCT
ejpam-5711	230	16	sxj(dxdy(ptn	sxj(dxdy(ptn	PROPN
ejpam-5711	230	17	)	)	PUNCT
ejpam-5711	230	18	)	)	PUNCT
ejpam-5711	231	1	=	=	PUNCT
ejpam-5711	231	2	(	(	PUNCT
ejpam-5711	231	3	1	1	NUM
ejpam-5711	231	4	+	+	NUM
ejpam-5711	231	5	2n)x4	2n)x4	NUM
ejpam-5711	231	6	+	+	CCONJ
ejpam-5711	231	7	4	4	NUM
ejpam-5711	231	8	3(2	3(2	NUM
ejpam-5711	231	9	+	+	CCONJ
ejpam-5711	231	10	2n+1)x6	2n+1)x6	NUM
ejpam-5711	231	11	+	+	CCONJ
ejpam-5711	231	12	2(5	2(5	NUM
ejpam-5711	231	13	·	·	PUNCT
ejpam-5711	231	14	2n	2n	NUM
ejpam-5711	231	15	−	−	ADP
ejpam-5711	231	16	7)x8	7)x8	NUM
ejpam-5711	231	17	,	,	PUNCT
ejpam-5711	231	18	dγ	dγ	ADP
ejpam-5711	231	19	xd	xd	ADV
ejpam-5711	231	20	γ	γ	PROPN
ejpam-5711	231	21	y	y	PROPN
ejpam-5711	231	22	(	(	PUNCT
ejpam-5711	231	23	ptn	ptn	PROPN
ejpam-5711	231	24	)	)	PUNCT
ejpam-5711	231	25	=	=	PUNCT
ejpam-5711	232	1	22γ(1	22γ(1	NUM
ejpam-5711	232	2	+	+	CCONJ
ejpam-5711	232	3	2n)x2y2	2n)x2y2	NUM
ejpam-5711	232	4	+	+	CCONJ
ejpam-5711	232	5	23γ(2	23γ(2	NUM
ejpam-5711	233	1	+	+	CCONJ
ejpam-5711	233	2	2n+1)x2y4	2n+1)x2y4	NUM
ejpam-5711	234	1	+	+	CCONJ
ejpam-5711	234	2	24γ(5	24γ(5	NUM
ejpam-5711	234	3	·	·	PUNCT
ejpam-5711	234	4	2n	2n	NUM
ejpam-5711	234	5	−	−	PROPN
ejpam-5711	234	6	7)x4y4	7)x4y4	NOUN
ejpam-5711	234	7	,	,	PUNCT
ejpam-5711	234	8	thus	thus	ADV
ejpam-5711	234	9	,	,	PUNCT
ejpam-5711	234	10	(	(	PUNCT
ejpam-5711	234	11	i	i	NOUN
ejpam-5711	234	12	)	)	PUNCT
ejpam-5711	234	13	m1(ptn	m1(ptn	PROPN
ejpam-5711	234	14	)	)	PUNCT
ejpam-5711	234	15	=	=	PUNCT
ejpam-5711	234	16	(	(	PUNCT
ejpam-5711	234	17	dx	dx	PROPN
ejpam-5711	234	18	+	+	PROPN
ejpam-5711	234	19	dy)(m(fgbn;x	dy)(m(fgbn;x	PROPN
ejpam-5711	234	20	,	,	PUNCT
ejpam-5711	234	21	y))|x	y))|x	PROPN
ejpam-5711	234	22	=	=	SYM
ejpam-5711	234	23	y=1	y=1	NOUN
ejpam-5711	234	24	=	=	SYM
ejpam-5711	234	25	56	56	NUM
ejpam-5711	234	26	·	·	SYM
ejpam-5711	234	27	2n	2n	NUM
ejpam-5711	234	28	−	−	NUM
ejpam-5711	234	29	40	40	NUM
ejpam-5711	234	30	.	.	PUNCT
ejpam-5711	235	1	(	(	PUNCT
ejpam-5711	235	2	ii	ii	NOUN
ejpam-5711	235	3	)	)	PUNCT
ejpam-5711	235	4	m2(ptn	m2(ptn	PROPN
ejpam-5711	235	5	)	)	PUNCT
ejpam-5711	235	6	=	=	SYM
ejpam-5711	235	7	(	(	PUNCT
ejpam-5711	235	8	dxdy)(m(fgbn;x	dxdy)(m(fgbn;x	PROPN
ejpam-5711	235	9	,	,	PUNCT
ejpam-5711	235	10	y))|x	y))|x	PROPN
ejpam-5711	235	11	=	=	SYM
ejpam-5711	235	12	y=1	y=1	NOUN
ejpam-5711	235	13	=	=	SYM
ejpam-5711	235	14	100	100	NUM
ejpam-5711	235	15	·	·	PUNCT
ejpam-5711	235	16	2n	2n	NUM
ejpam-5711	236	1	−	−	ADP
ejpam-5711	236	2	92	92	NUM
ejpam-5711	236	3	.	.	PUNCT
ejpam-5711	237	1	(	(	PUNCT
ejpam-5711	237	2	iii	iii	X
ejpam-5711	237	3	)	)	PUNCT
ejpam-5711	237	4	mm2(ptn	mm2(ptn	PROPN
ejpam-5711	237	5	)	)	PUNCT
ejpam-5711	238	1	=	=	SYM
ejpam-5711	238	2	(	(	PUNCT
ejpam-5711	238	3	sxsy)(m(fgbn;x	sxsy)(m(fgbn;x	NOUN
ejpam-5711	238	4	,	,	PUNCT
ejpam-5711	238	5	y))|x	y))|x	PROPN
ejpam-5711	238	6	=	=	SYM
ejpam-5711	238	7	y=1	y=1	NOUN
ejpam-5711	238	8	=	=	SYM
ejpam-5711	238	9	13	13	NUM
ejpam-5711	238	10	16	16	NUM
ejpam-5711	238	11	·	·	SYM
ejpam-5711	238	12	2n	2n	NUM
ejpam-5711	239	1	+	+	CCONJ
ejpam-5711	239	2	1	1	NUM
ejpam-5711	239	3	16	16	NUM
ejpam-5711	239	4	.	.	PUNCT
ejpam-5711	240	1	(	(	PUNCT
ejpam-5711	240	2	iv	iv	X
ejpam-5711	240	3	)	)	PUNCT
ejpam-5711	240	4	rγ(ptn	rγ(ptn	PROPN
ejpam-5711	240	5	)	)	PUNCT
ejpam-5711	241	1	=	=	PRON
ejpam-5711	241	2	(	(	PUNCT
ejpam-5711	241	3	dγ	dγ	NOUN
ejpam-5711	241	4	xd	xd	INTJ
ejpam-5711	241	5	γ	γ	PROPN
ejpam-5711	241	6	y	y	PROPN
ejpam-5711	241	7	)	)	PUNCT
ejpam-5711	241	8	(	(	PUNCT
ejpam-5711	241	9	m(fgbn;x	m(fgbn;x	PROPN
ejpam-5711	241	10	,	,	PUNCT
ejpam-5711	241	11	y))|x	y))|x	PROPN
ejpam-5711	241	12	=	=	SYM
ejpam-5711	241	13	y=1	y=1	NOUN
ejpam-5711	241	14	=	=	PUNCT
ejpam-5711	241	15	(	(	PUNCT
ejpam-5711	241	16	1	1	NUM
ejpam-5711	241	17	+	+	X
ejpam-5711	241	18	2γ+1	2γ+1	NUM
ejpam-5711	241	19	−	−	NUM
ejpam-5711	241	20	7	7	NUM
ejpam-5711	241	21	·	·	PUNCT
ejpam-5711	241	22	22γ)22γ	22γ)22γ	PROPN
ejpam-5711	242	1	+	+	CCONJ
ejpam-5711	242	2	(	(	PUNCT
ejpam-5711	242	3	1	1	NUM
ejpam-5711	242	4	+	+	CCONJ
ejpam-5711	242	5	2γ+1	2γ+1	NUM
ejpam-5711	242	6	+	+	CCONJ
ejpam-5711	242	7	5	5	NUM
ejpam-5711	242	8	·	·	SYM
ejpam-5711	242	9	22γ)22γ+n	22γ)22γ+n	NUM
ejpam-5711	242	10	.	.	PUNCT
ejpam-5711	243	1	(	(	PUNCT
ejpam-5711	243	2	v	v	NOUN
ejpam-5711	243	3	)	)	PUNCT
ejpam-5711	243	4	ssd(ptn	ssd(ptn	NOUN
ejpam-5711	243	5	)	)	PUNCT
ejpam-5711	244	1	=	=	SYM
ejpam-5711	244	2	(	(	PUNCT
ejpam-5711	244	3	sydx	sydx	NOUN
ejpam-5711	244	4	+	+	CCONJ
ejpam-5711	244	5	sxdy)(m(fgbn;x	sxdy)(m(fgbn;x	PROPN
ejpam-5711	244	6	,	,	PUNCT
ejpam-5711	244	7	y))|x	y))|x	PROPN
ejpam-5711	244	8	=	=	SYM
ejpam-5711	244	9	y=1	y=1	SYM
ejpam-5711	244	10	=	=	SYM
ejpam-5711	244	11	17	17	NUM
ejpam-5711	244	12	·	·	SYM
ejpam-5711	244	13	2n	2n	NUM
ejpam-5711	245	1	−	−	NOUN
ejpam-5711	245	2	7	7	X
ejpam-5711	245	3	.	.	PUNCT
ejpam-5711	245	4	(	(	PUNCT
ejpam-5711	245	5	vi	vi	NOUN
ejpam-5711	245	6	)	)	PUNCT
ejpam-5711	245	7	h(ptn	h(ptn	NOUN
ejpam-5711	245	8	)	)	PUNCT
ejpam-5711	245	9	=	=	SYM
ejpam-5711	245	10	(	(	PUNCT
ejpam-5711	245	11	2sxj)(m(fgbn	2sxj)(m(fgbn	NUM
ejpam-5711	245	12	;	;	PUNCT
ejpam-5711	245	13	x	x	X
ejpam-5711	245	14	,	,	PUNCT
ejpam-5711	245	15	y))|x=1	y))|x=1	PROPN
ejpam-5711	245	16	=	=	PUNCT
ejpam-5711	245	17	29	29	NUM
ejpam-5711	245	18	12(2	12(2	NUM
ejpam-5711	245	19	n)−	n)−	PROPN
ejpam-5711	245	20	7	7	NUM
ejpam-5711	245	21	12	12	NUM
ejpam-5711	245	22	.	.	PUNCT
ejpam-5711	246	1	(	(	PUNCT
ejpam-5711	246	2	vii	vii	PROPN
ejpam-5711	246	3	)	)	PUNCT
ejpam-5711	246	4	i(ptn	i(ptn	PROPN
ejpam-5711	246	5	)	)	PUNCT
ejpam-5711	246	6	=	=	SYM
ejpam-5711	246	7	sxj(dxdy(m(fgbn;x	sxj(dxdy(m(fgbn;x	PROPN
ejpam-5711	246	8	,	,	PUNCT
ejpam-5711	246	9	y)))|x=1	y)))|x=1	X
ejpam-5711	247	1	=	=	NOUN
ejpam-5711	248	1	41	41	NUM
ejpam-5711	248	2	3	3	NUM
ejpam-5711	248	3	2	2	NUM
ejpam-5711	248	4	n	n	NUM
ejpam-5711	248	5	−	−	PROPN
ejpam-5711	248	6	31	31	NUM
ejpam-5711	248	7	3	3	NUM
ejpam-5711	248	8	.	.	PUNCT
ejpam-5711	249	1	n.	n.	PROPN
ejpam-5711	249	2	t.	t.	PROPN
ejpam-5711	249	3	sarhan	sarhan	PROPN
ejpam-5711	249	4	,	,	PUNCT
ejpam-5711	249	5	d.	d.	PROPN
ejpam-5711	249	6	a.	a.	PROPN
ejpam-5711	249	7	ali	ali	PROPN
ejpam-5711	249	8	,	,	PUNCT
ejpam-5711	249	9	g.	g.	PROPN
ejpam-5711	249	10	h.	h.	PROPN
ejpam-5711	250	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	250	2	/	/	SYM
ejpam-5711	250	3	eur	eur	PROPN
ejpam-5711	250	4	.	.	PUNCT
ejpam-5711	251	1	j.	j.	PROPN
ejpam-5711	251	2	pure	pure	PROPN
ejpam-5711	251	3	appl	appl	PROPN
ejpam-5711	251	4	.	.	PROPN
ejpam-5711	251	5	math	math	PROPN
ejpam-5711	251	6	,	,	PUNCT
ejpam-5711	251	7	18	18	NUM
ejpam-5711	251	8	(	(	PUNCT
ejpam-5711	251	9	1	1	NUM
ejpam-5711	251	10	)	)	PUNCT
ejpam-5711	251	11	(	(	PUNCT
ejpam-5711	251	12	2025	2025	NUM
ejpam-5711	251	13	)	)	PUNCT
ejpam-5711	251	14	,	,	PUNCT
ejpam-5711	251	15	5711	5711	NUM
ejpam-5711	251	16	9	9	NUM
ejpam-5711	251	17	of	of	ADP
ejpam-5711	251	18	15	15	NUM
ejpam-5711	251	19	2.3	2.3	NUM
ejpam-5711	251	20	.	.	PUNCT
ejpam-5711	252	1	dendrimer	dendrimer	NOUN
ejpam-5711	252	2	of	of	ADP
ejpam-5711	252	3	benzene	benzene	NOUN
ejpam-5711	252	4	a	a	DET
ejpam-5711	252	5	dendrimer	dendrimer	NOUN
ejpam-5711	252	6	is	be	AUX
ejpam-5711	252	7	also	also	ADV
ejpam-5711	252	8	one	one	NUM
ejpam-5711	252	9	kind	kind	NOUN
ejpam-5711	252	10	of	of	ADP
ejpam-5711	252	11	a	a	DET
ejpam-5711	252	12	graph	graph	NOUN
ejpam-5711	252	13	that	that	PRON
ejpam-5711	252	14	is	be	AUX
ejpam-5711	252	15	never	never	ADV
ejpam-5711	252	16	-	-	PUNCT
ejpam-5711	252	17	ending	ending	NOUN
ejpam-5711	252	18	in	in	ADP
ejpam-5711	252	19	its	its	PRON
ejpam-5711	252	20	iterative	iterative	NOUN
ejpam-5711	252	21	growth	growth	NOUN
ejpam-5711	252	22	,	,	PUNCT
ejpam-5711	252	23	it	it	PRON
ejpam-5711	252	24	possesses	possess	VERB
ejpam-5711	252	25	molecular	molecular	ADJ
ejpam-5711	252	26	architecture	architecture	NOUN
ejpam-5711	252	27	has	have	VERB
ejpam-5711	252	28	three	three	NUM
ejpam-5711	252	29	domains	domain	NOUN
ejpam-5711	252	30	central	central	ADJ
ejpam-5711	252	31	,	,	PUNCT
ejpam-5711	252	32	branches	branch	NOUN
ejpam-5711	252	33	,	,	PUNCT
ejpam-5711	252	34	and	and	CCONJ
ejpam-5711	252	35	terminal	terminal	ADJ
ejpam-5711	252	36	.	.	PUNCT
ejpam-5711	253	1	as	as	SCONJ
ejpam-5711	253	2	shown	show	VERB
ejpam-5711	253	3	in	in	ADP
ejpam-5711	253	4	next	next	ADJ
ejpam-5711	253	5	figure	figure	NOUN
ejpam-5711	253	6	3	3	NUM
ejpam-5711	253	7	.	.	PUNCT
ejpam-5711	253	8	figure	figure	VERB
ejpam-5711	253	9	3	3	NUM
ejpam-5711	253	10	:	:	PUNCT
ejpam-5711	253	11	dendrimer	dendrimer	NOUN
ejpam-5711	253	12	of	of	ADP
ejpam-5711	253	13	benzene	benzene	ADJ
ejpam-5711	253	14	db1	db1	NOUN
ejpam-5711	253	15	,	,	PUNCT
ejpam-5711	253	16	db2	db2	PROPN
ejpam-5711	253	17	and	and	CCONJ
ejpam-5711	253	18	db3	db3	PROPN
ejpam-5711	253	19	.	.	PUNCT
ejpam-5711	254	1	m	m	NOUN
ejpam-5711	254	2	-	-	ADJ
ejpam-5711	254	3	polynomial	polynomial	ADJ
ejpam-5711	254	4	of	of	ADP
ejpam-5711	254	5	dendrimer	dendrimer	NOUN
ejpam-5711	254	6	graph	graph	NOUN
ejpam-5711	254	7	is	be	AUX
ejpam-5711	254	8	given	give	VERB
ejpam-5711	254	9	in	in	ADP
ejpam-5711	254	10	theorem	theorem	ADJ
ejpam-5711	254	11	3	3	NUM
ejpam-5711	254	12	.	.	PUNCT
ejpam-5711	254	13	theorem	theorem	NOUN
ejpam-5711	254	14	3	3	X
ejpam-5711	254	15	.	.	PUNCT
ejpam-5711	255	1	let	let	VERB
ejpam-5711	255	2	dbn	dbn	PROPN
ejpam-5711	255	3	be	be	AUX
ejpam-5711	255	4	a	a	DET
ejpam-5711	255	5	dendrimer	dendrimer	NOUN
ejpam-5711	255	6	of	of	ADP
ejpam-5711	255	7	benzene	benzene	NOUN
ejpam-5711	255	8	where	where	SCONJ
ejpam-5711	255	9	n	n	PRON
ejpam-5711	255	10	is	be	AUX
ejpam-5711	255	11	the	the	DET
ejpam-5711	255	12	number	number	NOUN
ejpam-5711	255	13	of	of	ADP
ejpam-5711	255	14	iterative	iterative	ADJ
ejpam-5711	255	15	growth	growth	NOUN
ejpam-5711	255	16	of	of	ADP
ejpam-5711	255	17	the	the	DET
ejpam-5711	255	18	dendrimer	dendrimer	NOUN
ejpam-5711	255	19	.	.	PUNCT
ejpam-5711	256	1	(	(	PUNCT
ejpam-5711	256	2	i	i	NOUN
ejpam-5711	256	3	)	)	PUNCT
ejpam-5711	256	4	if	if	SCONJ
ejpam-5711	256	5	n	n	NOUN
ejpam-5711	256	6	=	=	SYM
ejpam-5711	256	7	1	1	NUM
ejpam-5711	256	8	,	,	PUNCT
ejpam-5711	256	9	then	then	ADV
ejpam-5711	256	10	m(db1;x	m(db1;x	PROPN
ejpam-5711	256	11	,	,	PUNCT
ejpam-5711	256	12	y	y	NOUN
ejpam-5711	256	13	)	)	PUNCT
ejpam-5711	256	14	=	=	SYM
ejpam-5711	256	15	6x2y2	6x2y2	NUM
ejpam-5711	256	16	.	.	PUNCT
ejpam-5711	257	1	(	(	PUNCT
ejpam-5711	257	2	ii	ii	NOUN
ejpam-5711	257	3	)	)	PUNCT
ejpam-5711	257	4	if	if	SCONJ
ejpam-5711	257	5	n	n	PRON
ejpam-5711	257	6	≥	≥	NOUN
ejpam-5711	257	7	2	2	NUM
ejpam-5711	257	8	,	,	PUNCT
ejpam-5711	257	9	then	then	ADV
ejpam-5711	257	10	m(dbn;x	m(dbn;x	PROPN
ejpam-5711	257	11	,	,	PUNCT
ejpam-5711	257	12	y	y	NOUN
ejpam-5711	257	13	)	)	PUNCT
ejpam-5711	257	14	=	=	SYM
ejpam-5711	258	1	24(5n−2)x2y2	24(5n−2)x2y2	NUM
ejpam-5711	259	1	+	+	CCONJ
ejpam-5711	259	2	12(5n−2)x2y4	12(5n−2)x2y4	NUM
ejpam-5711	259	3	+	+	ADJ
ejpam-5711	259	4	(	(	PUNCT
ejpam-5711	259	5	9	9	NUM
ejpam-5711	259	6	·	·	SYM
ejpam-5711	259	7	5n−2	5n−2	NUM
ejpam-5711	259	8	−	−	NOUN
ejpam-5711	259	9	3)x4y4	3)x4y4	NOUN
ejpam-5711	259	10	.	.	PUNCT
ejpam-5711	260	1	proof	proof	NOUN
ejpam-5711	260	2	.	.	PUNCT
ejpam-5711	261	1	let	let	VERB
ejpam-5711	261	2	dbn	dbn	PROPN
ejpam-5711	261	3	,	,	PUNCT
ejpam-5711	261	4	n	n	PRON
ejpam-5711	261	5	≥	≥	NOUN
ejpam-5711	261	6	1	1	NUM
ejpam-5711	261	7	is	be	AUX
ejpam-5711	261	8	the	the	DET
ejpam-5711	261	9	dendrimer	dendrimer	NOUN
ejpam-5711	261	10	of	of	ADP
ejpam-5711	261	11	benzene	benzene	NOUN
ejpam-5711	261	12	as	as	SCONJ
ejpam-5711	261	13	shown	show	VERB
ejpam-5711	261	14	in	in	ADP
ejpam-5711	261	15	figure	figure	NOUN
ejpam-5711	261	16	3	3	NUM
ejpam-5711	261	17	,	,	PUNCT
ejpam-5711	261	18	then	then	ADV
ejpam-5711	261	19	|v(dbn)|	|v(dbn)|	ADP
ejpam-5711	261	20	=	=	SYM
ejpam-5711	261	21	3	3	NUM
ejpam-5711	261	22	2(5	2(5	NUM
ejpam-5711	261	23	n	n	CCONJ
ejpam-5711	261	24	−	−	NOUN
ejpam-5711	261	25	1	1	NUM
ejpam-5711	261	26	)	)	PUNCT
ejpam-5711	261	27	and	and	CCONJ
ejpam-5711	261	28	|e(dbn)|	|e(dbn)|	NOUN
ejpam-5711	261	29	=	=	SYM
ejpam-5711	261	30	6	6	NUM
ejpam-5711	261	31	+	+	SYM
ejpam-5711	261	32	9	9	NUM
ejpam-5711	261	33	·	·	SYM
ejpam-5711	261	34	5n−1	5n−1	NUM
ejpam-5711	261	35	−	−	NOUN
ejpam-5711	261	36	3	3	X
ejpam-5711	261	37	.	.	PUNCT
ejpam-5711	262	1	(	(	PUNCT
ejpam-5711	262	2	i	i	NOUN
ejpam-5711	262	3	)	)	PUNCT
ejpam-5711	262	4	for	for	ADP
ejpam-5711	262	5	n	n	NOUN
ejpam-5711	262	6	=	=	SYM
ejpam-5711	262	7	1	1	NUM
ejpam-5711	262	8	,	,	PUNCT
ejpam-5711	262	9	the	the	DET
ejpam-5711	262	10	prove	prove	NOUN
ejpam-5711	262	11	is	be	AUX
ejpam-5711	262	12	same	same	ADJ
ejpam-5711	262	13	as	as	ADP
ejpam-5711	262	14	in	in	ADP
ejpam-5711	262	15	theorem	theorem	NOUN
ejpam-5711	262	16	1	1	NUM
ejpam-5711	262	17	.	.	PUNCT
ejpam-5711	262	18	(	(	PUNCT
ejpam-5711	262	19	ii	ii	NOUN
ejpam-5711	262	20	)	)	PUNCT
ejpam-5711	262	21	for	for	ADP
ejpam-5711	262	22	n	n	X
ejpam-5711	262	23	≥	≥	NUM
ejpam-5711	262	24	2	2	NUM
ejpam-5711	262	25	,	,	PUNCT
ejpam-5711	262	26	the	the	DET
ejpam-5711	262	27	edge	edge	NOUN
ejpam-5711	262	28	set	set	VERB
ejpam-5711	262	29	e(dbn	e(dbn	NOUN
ejpam-5711	262	30	)	)	PUNCT
ejpam-5711	262	31	has	have	VERB
ejpam-5711	262	32	three	three	NUM
ejpam-5711	262	33	partitions	partition	NOUN
ejpam-5711	262	34	:	:	PUNCT
ejpam-5711	262	35	|e(2	|e(2	ADJ
ejpam-5711	262	36	,	,	PUNCT
ejpam-5711	262	37	2)|	2)|	NUM
ejpam-5711	263	1	=	=	SYM
ejpam-5711	263	2	|e	|e	NOUN
ejpam-5711	263	3	=	=	PUNCT
ejpam-5711	263	4	uv	uv	NOUN
ejpam-5711	263	5	∈	∈	PROPN
ejpam-5711	263	6	e(fgbn	e(fgbn	NOUN
ejpam-5711	263	7	)	)	PUNCT
ejpam-5711	263	8	:	:	PUNCT
ejpam-5711	264	1	du	du	PROPN
ejpam-5711	264	2	=	=	SYM
ejpam-5711	264	3	2	2	NUM
ejpam-5711	264	4	and	and	CCONJ
ejpam-5711	264	5	dv	dv	PROPN
ejpam-5711	265	1	=	=	PROPN
ejpam-5711	265	2	2|	2|	NUM
ejpam-5711	265	3	=	=	SYM
ejpam-5711	265	4	24(5n−2	24(5n−2	PROPN
ejpam-5711	265	5	)	)	PUNCT
ejpam-5711	265	6	.	.	PUNCT
ejpam-5711	266	1	|e(2	|e(2	NOUN
ejpam-5711	266	2	,	,	PUNCT
ejpam-5711	266	3	4)|	4)|	NUM
ejpam-5711	266	4	=	=	SYM
ejpam-5711	266	5	|e	|e	NOUN
ejpam-5711	267	1	=	=	PUNCT
ejpam-5711	267	2	uv	uv	NOUN
ejpam-5711	267	3	∈	∈	PROPN
ejpam-5711	267	4	e(fgbn	e(fgbn	NOUN
ejpam-5711	267	5	)	)	PUNCT
ejpam-5711	267	6	:	:	PUNCT
ejpam-5711	267	7	du	du	PROPN
ejpam-5711	267	8	=	=	SYM
ejpam-5711	267	9	2	2	NUM
ejpam-5711	267	10	and	and	CCONJ
ejpam-5711	267	11	dv	dv	PROPN
ejpam-5711	267	12	=	=	PROPN
ejpam-5711	267	13	4|	4|	NUM
ejpam-5711	267	14	=	=	SYM
ejpam-5711	268	1	12(5n−2	12(5n−2	NUM
ejpam-5711	268	2	)	)	PUNCT
ejpam-5711	268	3	.	.	PUNCT
ejpam-5711	269	1	|e(4	|e(4	NOUN
ejpam-5711	269	2	,	,	PUNCT
ejpam-5711	269	3	4)|	4)|	NUM
ejpam-5711	269	4	=	=	SYM
ejpam-5711	269	5	|e	|e	NOUN
ejpam-5711	270	1	=	=	PUNCT
ejpam-5711	270	2	uv	uv	NOUN
ejpam-5711	270	3	∈	∈	PROPN
ejpam-5711	270	4	e(fgbn	e(fgbn	NOUN
ejpam-5711	270	5	)	)	PUNCT
ejpam-5711	270	6	:	:	PUNCT
ejpam-5711	271	1	du	du	PROPN
ejpam-5711	271	2	=	=	SYM
ejpam-5711	271	3	4	4	NUM
ejpam-5711	271	4	and	and	CCONJ
ejpam-5711	271	5	dv	dv	PROPN
ejpam-5711	271	6	=	=	PUNCT
ejpam-5711	271	7	4|	4|	NUM
ejpam-5711	272	1	=	=	SYM
ejpam-5711	272	2	6	6	NUM
ejpam-5711	272	3	+	+	CCONJ
ejpam-5711	272	4	9	9	NUM
ejpam-5711	272	5	·	·	SYM
ejpam-5711	272	6	5n−2	5n−2	NUM
ejpam-5711	272	7	−	−	NOUN
ejpam-5711	272	8	3	3	X
ejpam-5711	272	9	.	.	PUNCT
ejpam-5711	272	10	n.	n.	PROPN
ejpam-5711	272	11	t.	t.	PROPN
ejpam-5711	272	12	sarhan	sarhan	PROPN
ejpam-5711	272	13	,	,	PUNCT
ejpam-5711	272	14	d.	d.	PROPN
ejpam-5711	272	15	a.	a.	PROPN
ejpam-5711	272	16	ali	ali	PROPN
ejpam-5711	272	17	,	,	PUNCT
ejpam-5711	272	18	g.	g.	PROPN
ejpam-5711	272	19	h.	h.	PROPN
ejpam-5711	273	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	273	2	/	/	SYM
ejpam-5711	273	3	eur	eur	PROPN
ejpam-5711	273	4	.	.	PUNCT
ejpam-5711	274	1	j.	j.	PROPN
ejpam-5711	274	2	pure	pure	PROPN
ejpam-5711	274	3	appl	appl	PROPN
ejpam-5711	274	4	.	.	PROPN
ejpam-5711	274	5	math	math	PROPN
ejpam-5711	274	6	,	,	PUNCT
ejpam-5711	274	7	18	18	NUM
ejpam-5711	274	8	(	(	PUNCT
ejpam-5711	274	9	1	1	NUM
ejpam-5711	274	10	)	)	PUNCT
ejpam-5711	274	11	(	(	PUNCT
ejpam-5711	274	12	2025	2025	NUM
ejpam-5711	274	13	)	)	PUNCT
ejpam-5711	274	14	,	,	PUNCT
ejpam-5711	274	15	5711	5711	NUM
ejpam-5711	274	16	10	10	NUM
ejpam-5711	274	17	of	of	ADP
ejpam-5711	274	18	15	15	NUM
ejpam-5711	274	19	hence	hence	ADV
ejpam-5711	274	20	,	,	PUNCT
ejpam-5711	274	21	the	the	DET
ejpam-5711	274	22	m	m	NOUN
ejpam-5711	274	23	-	-	ADJ
ejpam-5711	274	24	polynomial	polynomial	ADJ
ejpam-5711	274	25	of	of	ADP
ejpam-5711	274	26	dbn	dbn	PROPN
ejpam-5711	274	27	is	be	AUX
ejpam-5711	274	28	m(dbn;x	m(dbn;x	PROPN
ejpam-5711	274	29	,	,	PUNCT
ejpam-5711	274	30	y	y	NOUN
ejpam-5711	274	31	)	)	PUNCT
ejpam-5711	274	32	=	=	PUNCT
ejpam-5711	274	33	∑	∑	PUNCT
ejpam-5711	274	34	δ≤α≤β≤∆	δ≤α≤β≤∆	PROPN
ejpam-5711	274	35	mα	mα	PROPN
ejpam-5711	274	36	,	,	PUNCT
ejpam-5711	274	37	βx	βx	AUX
ejpam-5711	274	38	αyβ	αyβ	VERB
ejpam-5711	274	39	=	=	PUNCT
ejpam-5711	274	40	∑	∑	PUNCT
ejpam-5711	274	41	2≤2	2≤2	NUM
ejpam-5711	274	42	m2,2x	m2,2x	NOUN
ejpam-5711	274	43	2y2	2y2	NUM
ejpam-5711	274	44	+	+	CCONJ
ejpam-5711	274	45	∑	∑	PUNCT
ejpam-5711	274	46	2≤4	2≤4	SYM
ejpam-5711	274	47	m2,4x	m2,4x	PROPN
ejpam-5711	274	48	2y4	2y4	NUM
ejpam-5711	275	1	+	+	CCONJ
ejpam-5711	275	2	∑	∑	PUNCT
ejpam-5711	275	3	4≤4	4≤4	NUM
ejpam-5711	275	4	m4,4x	m4,4x	PROPN
ejpam-5711	275	5	4y4	4y4	NUM
ejpam-5711	276	1	=	=	SYM
ejpam-5711	276	2	24(5n−2)x2y2	24(5n−2)x2y2	NUM
ejpam-5711	277	1	+	+	CCONJ
ejpam-5711	277	2	12(5n−2)x2y4	12(5n−2)x2y4	NUM
ejpam-5711	277	3	+	+	CCONJ
ejpam-5711	278	1	[	[	X
ejpam-5711	278	2	6	6	NUM
ejpam-5711	278	3	+	+	NUM
ejpam-5711	278	4	9(5n−2	9(5n−2	NUM
ejpam-5711	278	5	−	−	NOUN
ejpam-5711	278	6	1)]x4y4	1)]x4y4	NUM
ejpam-5711	278	7	.	.	PUNCT
ejpam-5711	279	1	the	the	DET
ejpam-5711	279	2	following	follow	VERB
ejpam-5711	279	3	proposition	proposition	NOUN
ejpam-5711	279	4	provides	provide	VERB
ejpam-5711	279	5	the	the	DET
ejpam-5711	279	6	degree	degree	NOUN
ejpam-5711	279	7	-	-	PUNCT
ejpam-5711	279	8	based	base	VERB
ejpam-5711	279	9	topological	topological	ADJ
ejpam-5711	279	10	indices	index	NOUN
ejpam-5711	279	11	for	for	ADP
ejpam-5711	279	12	the	the	DET
ejpam-5711	279	13	benzene	benzene	NOUN
ejpam-5711	279	14	dendrimer	dendrimer	PROPN
ejpam-5711	279	15	dbn	dbn	PROPN
ejpam-5711	279	16	,	,	PUNCT
ejpam-5711	279	17	n	n	PRON
ejpam-5711	279	18	≥	≥	NOUN
ejpam-5711	279	19	2	2	NUM
ejpam-5711	279	20	.	.	PUNCT
ejpam-5711	279	21	proposition	proposition	NOUN
ejpam-5711	279	22	3	3	NUM
ejpam-5711	279	23	.	.	PUNCT
ejpam-5711	280	1	let	let	VERB
ejpam-5711	280	2	dbn	dbn	PROPN
ejpam-5711	280	3	be	be	AUX
ejpam-5711	280	4	a	a	DET
ejpam-5711	280	5	dendrimer	dendrimer	NOUN
ejpam-5711	280	6	of	of	ADP
ejpam-5711	280	7	benzene	benzene	NOUN
ejpam-5711	280	8	where	where	SCONJ
ejpam-5711	280	9	n	n	PRON
ejpam-5711	280	10	≥	≥	NOUN
ejpam-5711	280	11	2	2	NUM
ejpam-5711	280	12	,	,	PUNCT
ejpam-5711	280	13	then	then	ADV
ejpam-5711	280	14	(	(	PUNCT
ejpam-5711	280	15	i	i	NOUN
ejpam-5711	280	16	)	)	PUNCT
ejpam-5711	280	17	m1(dbn	m1(dbn	NUM
ejpam-5711	280	18	)	)	PUNCT
ejpam-5711	281	1	=	=	SYM
ejpam-5711	282	1	48(5n−1)−	48(5n−1)−	NUM
ejpam-5711	282	2	24	24	NUM
ejpam-5711	282	3	.	.	PUNCT
ejpam-5711	283	1	(	(	PUNCT
ejpam-5711	283	2	ii	ii	NOUN
ejpam-5711	283	3	)	)	PUNCT
ejpam-5711	283	4	m2(dbn	m2(dbn	ADV
ejpam-5711	283	5	)	)	PUNCT
ejpam-5711	284	1	=	=	PUNCT
ejpam-5711	285	1	336(5n−2)−	336(5n−2)−	NUM
ejpam-5711	285	2	48	48	NUM
ejpam-5711	285	3	.	.	PUNCT
ejpam-5711	286	1	(	(	PUNCT
ejpam-5711	286	2	iii	iii	NOUN
ejpam-5711	286	3	)	)	PUNCT
ejpam-5711	286	4	mm2(dbn	mm2(dbn	NOUN
ejpam-5711	286	5	)	)	PUNCT
ejpam-5711	286	6	=	=	NOUN
ejpam-5711	287	1	129	129	NUM
ejpam-5711	287	2	16	16	NUM
ejpam-5711	287	3	(	(	PUNCT
ejpam-5711	287	4	5	5	NUM
ejpam-5711	287	5	n−2)−	n−2)−	VERB
ejpam-5711	287	6	3	3	NUM
ejpam-5711	287	7	16	16	NUM
ejpam-5711	287	8	.	.	PUNCT
ejpam-5711	288	1	(	(	PUNCT
ejpam-5711	288	2	iv	iv	X
ejpam-5711	288	3	)	)	PUNCT
ejpam-5711	288	4	rγ(dbn	rγ(dbn	NOUN
ejpam-5711	288	5	)	)	PUNCT
ejpam-5711	289	1	=	=	SYM
ejpam-5711	289	2	3	3	NUM
ejpam-5711	289	3	·	·	SYM
ejpam-5711	289	4	22γ	22γ	NUM
ejpam-5711	289	5	·	·	PUNCT
ejpam-5711	289	6	5n−2[8	5n−2[8	NUM
ejpam-5711	289	7	+	+	NUM
ejpam-5711	289	8	2γ+2	2γ+2	NUM
ejpam-5711	289	9	+	+	CCONJ
ejpam-5711	289	10	3	3	NUM
ejpam-5711	289	11	·	·	SYM
ejpam-5711	289	12	22γ	22γ	NUM
ejpam-5711	289	13	]	]	SYM
ejpam-5711	289	14	−	−	PROPN
ejpam-5711	289	15	3	3	NUM
ejpam-5711	289	16	·	·	PUNCT
ejpam-5711	289	17	24γ	24γ	NUM
ejpam-5711	289	18	.	.	PUNCT
ejpam-5711	290	1	(	(	PUNCT
ejpam-5711	290	2	v	v	NOUN
ejpam-5711	290	3	)	)	PUNCT
ejpam-5711	290	4	ssd(dbn	ssd(dbn	NOUN
ejpam-5711	290	5	)	)	PUNCT
ejpam-5711	291	1	=	=	PRON
ejpam-5711	291	2	96(5n−2)−	96(5n−2)−	NUM
ejpam-5711	291	3	6	6	NUM
ejpam-5711	291	4	.	.	PUNCT
ejpam-5711	291	5	(	(	PUNCT
ejpam-5711	291	6	vi	vi	NOUN
ejpam-5711	291	7	)	)	PUNCT
ejpam-5711	291	8	h(dbn	h(dbn	NOUN
ejpam-5711	291	9	)	)	PUNCT
ejpam-5711	291	10	=	=	PUNCT
ejpam-5711	292	1	73	73	NUM
ejpam-5711	292	2	4	4	NUM
ejpam-5711	292	3	(	(	PUNCT
ejpam-5711	292	4	5	5	NUM
ejpam-5711	292	5	n−2)−	n−2)−	VERB
ejpam-5711	292	6	3	3	NUM
ejpam-5711	292	7	4	4	NUM
ejpam-5711	292	8	.	.	PUNCT
ejpam-5711	293	1	(	(	PUNCT
ejpam-5711	293	2	vii	vii	PROPN
ejpam-5711	293	3	)	)	PUNCT
ejpam-5711	293	4	i(dbn	i(dbn	PROPN
ejpam-5711	293	5	)	)	PUNCT
ejpam-5711	294	1	=	=	PUNCT
ejpam-5711	294	2	58(5n−2)−	58(5n−2)−	NUM
ejpam-5711	294	3	6	6	NUM
ejpam-5711	294	4	.	.	PUNCT
ejpam-5711	295	1	proof	proof	NOUN
ejpam-5711	295	2	.	.	PUNCT
ejpam-5711	296	1	since	since	SCONJ
ejpam-5711	296	2	,	,	PUNCT
ejpam-5711	296	3	m(dbn;x	m(dbn;x	PROPN
ejpam-5711	296	4	,	,	PUNCT
ejpam-5711	296	5	y	y	NOUN
ejpam-5711	296	6	)	)	PUNCT
ejpam-5711	296	7	=	=	PUNCT
ejpam-5711	297	1	24(5n−2)x2y2	24(5n−2)x2y2	NUM
ejpam-5711	297	2	+	+	ADJ
ejpam-5711	297	3	12(5n−2)x2y4+(9	12(5n−2)x2y4+(9	NUM
ejpam-5711	297	4	·	·	SYM
ejpam-5711	297	5	5n−2−3)x4y4	5n−2−3)x4y4	NOUN
ejpam-5711	297	6	.	.	PROPN
ejpam-5711	297	7	,	,	PUNCT
ejpam-5711	297	8	using	use	VERB
ejpam-5711	297	9	above	above	ADP
ejpam-5711	297	10	operators	operator	NOUN
ejpam-5711	297	11	we	we	PRON
ejpam-5711	297	12	get	get	VERB
ejpam-5711	297	13	:	:	PUNCT
ejpam-5711	297	14	dx(dbn	dx(dbn	NOUN
ejpam-5711	297	15	)	)	PUNCT
ejpam-5711	297	16	=	=	PUNCT
ejpam-5711	298	1	48(5n−2)x2y2	48(5n−2)x2y2	NUM
ejpam-5711	299	1	+	+	NUM
ejpam-5711	299	2	24(5n−2)x2y4	24(5n−2)x2y4	NUM
ejpam-5711	299	3	+	+	CCONJ
ejpam-5711	299	4	4(9	4(9	NUM
ejpam-5711	299	5	·	·	PUNCT
ejpam-5711	300	1	5n−2	5n−2	X
ejpam-5711	300	2	−	−	NOUN
ejpam-5711	300	3	3)x4y4	3)x4y4	NOUN
ejpam-5711	300	4	.	.	PUNCT
ejpam-5711	300	5	,	,	PUNCT
ejpam-5711	300	6	dy(dbn	dy(dbn	PROPN
ejpam-5711	300	7	)	)	PUNCT
ejpam-5711	300	8	=	=	PUNCT
ejpam-5711	301	1	48(5n−2)x2y2	48(5n−2)x2y2	NUM
ejpam-5711	302	1	+	+	PUNCT
ejpam-5711	302	2	48(5n−2)x2y4	48(5n−2)x2y4	NUM
ejpam-5711	303	1	+	+	CCONJ
ejpam-5711	303	2	4(9	4(9	NUM
ejpam-5711	303	3	·	·	PUNCT
ejpam-5711	304	1	5n−2	5n−2	X
ejpam-5711	304	2	−	−	NOUN
ejpam-5711	304	3	3)x4y4	3)x4y4	NOUN
ejpam-5711	304	4	.	.	PUNCT
ejpam-5711	304	5	,	,	PUNCT
ejpam-5711	304	6	dxdy(dbn	dxdy(dbn	NOUN
ejpam-5711	304	7	)	)	PUNCT
ejpam-5711	305	1	=	=	SYM
ejpam-5711	306	1	96(5n−2)x2y2	96(5n−2)x2y2	NUM
ejpam-5711	306	2	+	+	CCONJ
ejpam-5711	306	3	96(5n−2)x2y4	96(5n−2)x2y4	NUM
ejpam-5711	306	4	+	+	NUM
ejpam-5711	306	5	16(9	16(9	NUM
ejpam-5711	306	6	·	·	SYM
ejpam-5711	306	7	5n−2	5n−2	NUM
ejpam-5711	306	8	−	−	NOUN
ejpam-5711	306	9	3)x4y4	3)x4y4	NOUN
ejpam-5711	306	10	.	.	PUNCT
ejpam-5711	306	11	,	,	PUNCT
ejpam-5711	306	12	sx(dbn	sx(dbn	NOUN
ejpam-5711	306	13	)	)	PUNCT
ejpam-5711	306	14	=	=	SYM
ejpam-5711	307	1	12(5n−2)x2y2	12(5n−2)x2y2	NUM
ejpam-5711	308	1	+	+	NUM
ejpam-5711	308	2	6(5n−2)x2y4	6(5n−2)x2y4	NUM
ejpam-5711	309	1	+	+	CCONJ
ejpam-5711	309	2	1	1	NUM
ejpam-5711	309	3	4(9	4(9	NUM
ejpam-5711	309	4	·	·	PUNCT
ejpam-5711	309	5	5	5	NUM
ejpam-5711	309	6	n−2	n−2	PROPN
ejpam-5711	309	7	−	−	PROPN
ejpam-5711	309	8	3)x4y4	3)x4y4	NOUN
ejpam-5711	309	9	.	.	PUNCT
ejpam-5711	309	10	,	,	PUNCT
ejpam-5711	309	11	sy(dbn	sy(dbn	PROPN
ejpam-5711	309	12	)	)	PUNCT
ejpam-5711	309	13	=	=	PUNCT
ejpam-5711	310	1	12(5n−2)x2y2	12(5n−2)x2y2	NUM
ejpam-5711	311	1	+	+	NUM
ejpam-5711	311	2	3(5n−2)x2y4	3(5n−2)x2y4	NUM
ejpam-5711	311	3	+	+	CCONJ
ejpam-5711	311	4	1	1	NUM
ejpam-5711	311	5	4(9	4(9	NUM
ejpam-5711	311	6	·	·	PUNCT
ejpam-5711	311	7	5	5	NUM
ejpam-5711	311	8	n−2	n−2	PROPN
ejpam-5711	311	9	−	−	PROPN
ejpam-5711	311	10	3)x4y4	3)x4y4	NOUN
ejpam-5711	311	11	.	.	PUNCT
ejpam-5711	311	12	,	,	PUNCT
ejpam-5711	311	13	sxsy(dbn	sxsy(dbn	NOUN
ejpam-5711	311	14	)	)	PUNCT
ejpam-5711	311	15	=	=	PUNCT
ejpam-5711	312	1	6(5n−2)x2y2	6(5n−2)x2y2	NUM
ejpam-5711	312	2	+	+	CCONJ
ejpam-5711	312	3	3	3	NUM
ejpam-5711	312	4	2(5	2(5	NUM
ejpam-5711	312	5	n−2)x2y4	n−2)x2y4	PROPN
ejpam-5711	312	6	+	+	CCONJ
ejpam-5711	313	1	1	1	NUM
ejpam-5711	313	2	16(9	16(9	NUM
ejpam-5711	313	3	·	·	SYM
ejpam-5711	313	4	5	5	NUM
ejpam-5711	313	5	n−2	n−2	PROPN
ejpam-5711	313	6	−	−	PROPN
ejpam-5711	313	7	3)x4y4	3)x4y4	NOUN
ejpam-5711	313	8	.	.	PUNCT
ejpam-5711	313	9	,	,	PUNCT
ejpam-5711	313	10	sxdy(dbn	sxdy(dbn	ADJ
ejpam-5711	313	11	)	)	PUNCT
ejpam-5711	313	12	=	=	SYM
ejpam-5711	314	1	24(5n−2)x2y2	24(5n−2)x2y2	NUM
ejpam-5711	315	1	+	+	CCONJ
ejpam-5711	315	2	24(5n−2)x2y4	24(5n−2)x2y4	NUM
ejpam-5711	315	3	+	+	CCONJ
ejpam-5711	315	4	(	(	PUNCT
ejpam-5711	315	5	9	9	NUM
ejpam-5711	315	6	·	·	SYM
ejpam-5711	315	7	5n−2	5n−2	NUM
ejpam-5711	315	8	−	−	NOUN
ejpam-5711	315	9	3)x4y4	3)x4y4	NOUN
ejpam-5711	315	10	.	.	PUNCT
ejpam-5711	315	11	,	,	PUNCT
ejpam-5711	315	12	sydx(dbn	sydx(dbn	NOUN
ejpam-5711	315	13	)	)	PUNCT
ejpam-5711	315	14	=	=	SYM
ejpam-5711	316	1	24(5n−2)x2y2	24(5n−2)x2y2	NUM
ejpam-5711	317	1	+	+	CCONJ
ejpam-5711	317	2	6(5n−2)x2y4	6(5n−2)x2y4	NUM
ejpam-5711	317	3	+	+	CCONJ
ejpam-5711	317	4	(	(	PUNCT
ejpam-5711	317	5	9	9	NUM
ejpam-5711	317	6	·	·	SYM
ejpam-5711	317	7	5n−2	5n−2	NUM
ejpam-5711	317	8	−	−	NOUN
ejpam-5711	317	9	3)x4y4	3)x4y4	NOUN
ejpam-5711	317	10	.	.	PUNCT
ejpam-5711	317	11	,	,	PUNCT
ejpam-5711	317	12	sxj(dbn	sxj(dbn	NOUN
ejpam-5711	317	13	)	)	PUNCT
ejpam-5711	317	14	=	=	PUNCT
ejpam-5711	318	1	6(5n−2)x2y2	6(5n−2)x2y2	NUM
ejpam-5711	318	2	+	+	CCONJ
ejpam-5711	318	3	2(5n−2)x2y4	2(5n−2)x2y4	NUM
ejpam-5711	318	4	+	+	CCONJ
ejpam-5711	318	5	1	1	NUM
ejpam-5711	318	6	8(9	8(9	NUM
ejpam-5711	318	7	·	·	SYM
ejpam-5711	318	8	5	5	NUM
ejpam-5711	318	9	n−2	n−2	PROPN
ejpam-5711	318	10	−	−	PROPN
ejpam-5711	318	11	3)x4y4	3)x4y4	NOUN
ejpam-5711	318	12	.	.	PUNCT
ejpam-5711	318	13	,	,	PUNCT
ejpam-5711	318	14	sxj(dxdy(dbn	sxj(dxdy(dbn	NOUN
ejpam-5711	318	15	)	)	PUNCT
ejpam-5711	318	16	)	)	PUNCT
ejpam-5711	319	1	=	=	SYM
ejpam-5711	320	1	24(5n−2)x2y2	24(5n−2)x2y2	NUM
ejpam-5711	321	1	+	+	NUM
ejpam-5711	321	2	16(5n−2)x2y4	16(5n−2)x2y4	NUM
ejpam-5711	321	3	+	+	NUM
ejpam-5711	321	4	2(9	2(9	NUM
ejpam-5711	321	5	·	·	PUNCT
ejpam-5711	321	6	5n−2	5n−2	X
ejpam-5711	321	7	−	−	NOUN
ejpam-5711	321	8	3)x4y4	3)x4y4	NOUN
ejpam-5711	321	9	.	.	PUNCT
ejpam-5711	322	1	,	,	PUNCT
ejpam-5711	322	2	dγ	dγ	ADP
ejpam-5711	322	3	xd	xd	ADV
ejpam-5711	322	4	γ	γ	PROPN
ejpam-5711	322	5	y	y	PROPN
ejpam-5711	322	6	(	(	PUNCT
ejpam-5711	322	7	dbn	dbn	PROPN
ejpam-5711	322	8	)	)	PUNCT
ejpam-5711	322	9	=	=	SYM
ejpam-5711	322	10	3	3	NUM
ejpam-5711	322	11	·	·	SYM
ejpam-5711	322	12	22γ+3	22γ+3	NUM
ejpam-5711	322	13	·	·	PUNCT
ejpam-5711	322	14	5n−2x2y2	5n−2x2y2	NUM
ejpam-5711	322	15	+	+	CCONJ
ejpam-5711	322	16	3	3	NUM
ejpam-5711	322	17	·	·	SYM
ejpam-5711	322	18	23γ+2	23γ+2	NUM
ejpam-5711	322	19	·	·	PUNCT
ejpam-5711	323	1	5n−2x2y4	5n−2x2y4	NUM
ejpam-5711	323	2	+	+	CCONJ
ejpam-5711	323	3	24γ(9	24γ(9	NUM
ejpam-5711	323	4	·	·	PUNCT
ejpam-5711	323	5	5n−2	5n−2	NUM
ejpam-5711	323	6	−	−	NOUN
ejpam-5711	323	7	3)x4y4	3)x4y4	NOUN
ejpam-5711	323	8	..	..	PUNCT
ejpam-5711	323	9	thus	thus	ADV
ejpam-5711	323	10	,	,	PUNCT
ejpam-5711	323	11	n.	n.	PROPN
ejpam-5711	323	12	t.	t.	PROPN
ejpam-5711	323	13	sarhan	sarhan	PROPN
ejpam-5711	323	14	,	,	PUNCT
ejpam-5711	323	15	d.	d.	PROPN
ejpam-5711	323	16	a.	a.	PROPN
ejpam-5711	323	17	ali	ali	PROPN
ejpam-5711	323	18	,	,	PUNCT
ejpam-5711	323	19	g.	g.	PROPN
ejpam-5711	323	20	h.	h.	PROPN
ejpam-5711	324	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	324	2	/	/	SYM
ejpam-5711	324	3	eur	eur	PROPN
ejpam-5711	324	4	.	.	PUNCT
ejpam-5711	325	1	j.	j.	PROPN
ejpam-5711	325	2	pure	pure	PROPN
ejpam-5711	325	3	appl	appl	PROPN
ejpam-5711	325	4	.	.	PROPN
ejpam-5711	325	5	math	math	PROPN
ejpam-5711	325	6	,	,	PUNCT
ejpam-5711	325	7	18	18	NUM
ejpam-5711	325	8	(	(	PUNCT
ejpam-5711	325	9	1	1	NUM
ejpam-5711	325	10	)	)	PUNCT
ejpam-5711	325	11	(	(	PUNCT
ejpam-5711	325	12	2025	2025	NUM
ejpam-5711	325	13	)	)	PUNCT
ejpam-5711	325	14	,	,	PUNCT
ejpam-5711	325	15	5711	5711	NUM
ejpam-5711	325	16	11	11	NUM
ejpam-5711	325	17	of	of	ADP
ejpam-5711	325	18	15	15	NUM
ejpam-5711	325	19	(	(	PUNCT
ejpam-5711	325	20	i	i	NOUN
ejpam-5711	325	21	)	)	PUNCT
ejpam-5711	325	22	m1(fgbn	m1(fgbn	NOUN
ejpam-5711	325	23	)	)	PUNCT
ejpam-5711	325	24	=	=	PUNCT
ejpam-5711	325	25	(	(	PUNCT
ejpam-5711	325	26	dx	dx	PROPN
ejpam-5711	325	27	+	+	PROPN
ejpam-5711	325	28	dy)(m(fgbn;x	dy)(m(fgbn;x	PROPN
ejpam-5711	325	29	,	,	PUNCT
ejpam-5711	325	30	y))|x	y))|x	PROPN
ejpam-5711	325	31	=	=	SYM
ejpam-5711	325	32	y=1	y=1	NOUN
ejpam-5711	325	33	=	=	SYM
ejpam-5711	325	34	48(5n−1)−	48(5n−1)−	NUM
ejpam-5711	325	35	24	24	NUM
ejpam-5711	325	36	.	.	PUNCT
ejpam-5711	326	1	(	(	PUNCT
ejpam-5711	326	2	ii	ii	NOUN
ejpam-5711	326	3	)	)	PUNCT
ejpam-5711	326	4	m2(fgbn	m2(fgbn	NOUN
ejpam-5711	326	5	)	)	PUNCT
ejpam-5711	327	1	=	=	PRON
ejpam-5711	327	2	(	(	PUNCT
ejpam-5711	327	3	dxdy)(m(fgbn;x	dxdy)(m(fgbn;x	PROPN
ejpam-5711	327	4	,	,	PUNCT
ejpam-5711	327	5	y))|x	y))|x	PROPN
ejpam-5711	327	6	=	=	SYM
ejpam-5711	327	7	y=1	y=1	NOUN
ejpam-5711	327	8	=	=	SYM
ejpam-5711	328	1	336(5n−2)−	336(5n−2)−	NUM
ejpam-5711	328	2	48	48	NUM
ejpam-5711	328	3	.	.	PUNCT
ejpam-5711	329	1	(	(	PUNCT
ejpam-5711	329	2	iii	iii	NOUN
ejpam-5711	329	3	)	)	PUNCT
ejpam-5711	329	4	mm2(fgbn	mm2(fgbn	NOUN
ejpam-5711	329	5	)	)	PUNCT
ejpam-5711	330	1	=	=	SYM
ejpam-5711	330	2	(	(	PUNCT
ejpam-5711	330	3	sxsy)(m(fgbn;x	sxsy)(m(fgbn;x	NOUN
ejpam-5711	330	4	,	,	PUNCT
ejpam-5711	330	5	y))|x	y))|x	PROPN
ejpam-5711	330	6	=	=	SYM
ejpam-5711	330	7	y=1	y=1	SYM
ejpam-5711	330	8	=	=	SYM
ejpam-5711	330	9	129	129	NUM
ejpam-5711	330	10	16	16	NUM
ejpam-5711	330	11	(	(	PUNCT
ejpam-5711	330	12	5	5	NUM
ejpam-5711	330	13	n−2)−	n−2)−	VERB
ejpam-5711	330	14	3	3	NUM
ejpam-5711	330	15	16	16	NUM
ejpam-5711	330	16	.	.	PUNCT
ejpam-5711	331	1	(	(	PUNCT
ejpam-5711	331	2	iv	iv	X
ejpam-5711	331	3	)	)	PUNCT
ejpam-5711	331	4	rγ(fgbn	rγ(fgbn	PROPN
ejpam-5711	331	5	)	)	PUNCT
ejpam-5711	332	1	=	=	PRON
ejpam-5711	332	2	(	(	PUNCT
ejpam-5711	332	3	dγ	dγ	NOUN
ejpam-5711	332	4	xd	xd	INTJ
ejpam-5711	332	5	γ	γ	PROPN
ejpam-5711	332	6	y	y	PROPN
ejpam-5711	332	7	)	)	PUNCT
ejpam-5711	332	8	(	(	PUNCT
ejpam-5711	332	9	m(fgbn;x	m(fgbn;x	PROPN
ejpam-5711	332	10	,	,	PUNCT
ejpam-5711	332	11	y))|x	y))|x	PROPN
ejpam-5711	332	12	=	=	SYM
ejpam-5711	332	13	y=1	y=1	NOUN
ejpam-5711	332	14	=	=	SYM
ejpam-5711	332	15	3·22γ	3·22γ	PROPN
ejpam-5711	332	16	·	·	SYM
ejpam-5711	332	17	5n−2[8	5n−2[8	PROPN
ejpam-5711	332	18	+	+	NOUN
ejpam-5711	332	19	2γ+2	2γ+2	PROPN
ejpam-5711	332	20	+	+	SYM
ejpam-5711	332	21	3·22γ	3·22γ	NOUN
ejpam-5711	332	22	]	]	X
ejpam-5711	332	23	−3·24γ	−3·24γ	PROPN
ejpam-5711	332	24	.	.	PUNCT
ejpam-5711	333	1	(	(	PUNCT
ejpam-5711	333	2	v	v	NOUN
ejpam-5711	333	3	)	)	PUNCT
ejpam-5711	333	4	ssd(fgbn	ssd(fgbn	NOUN
ejpam-5711	333	5	)	)	PUNCT
ejpam-5711	333	6	=	=	PUNCT
ejpam-5711	334	1	(	(	PUNCT
ejpam-5711	334	2	sydx	sydx	NOUN
ejpam-5711	334	3	+	+	CCONJ
ejpam-5711	334	4	sxdy)(m(fgbn;x	sxdy)(m(fgbn;x	PROPN
ejpam-5711	334	5	,	,	PUNCT
ejpam-5711	334	6	y))|x	y))|x	PROPN
ejpam-5711	334	7	=	=	SYM
ejpam-5711	334	8	y=1	y=1	SYM
ejpam-5711	334	9	=	=	SYM
ejpam-5711	334	10	96(5n−2)−	96(5n−2)−	NUM
ejpam-5711	334	11	6	6	NUM
ejpam-5711	334	12	.	.	PUNCT
ejpam-5711	334	13	(	(	PUNCT
ejpam-5711	334	14	vi	vi	NOUN
ejpam-5711	334	15	)	)	PUNCT
ejpam-5711	334	16	h(fgbn	h(fgbn	NOUN
ejpam-5711	334	17	)	)	PUNCT
ejpam-5711	334	18	=	=	PUNCT
ejpam-5711	334	19	(	(	PUNCT
ejpam-5711	334	20	2sxj)(m(fgbn	2sxj)(m(fgbn	NUM
ejpam-5711	334	21	;	;	PUNCT
ejpam-5711	334	22	x	x	X
ejpam-5711	334	23	,	,	PUNCT
ejpam-5711	334	24	y))|x=1	y))|x=1	PROPN
ejpam-5711	334	25	=	=	NOUN
ejpam-5711	334	26	73	73	NUM
ejpam-5711	334	27	4	4	NUM
ejpam-5711	334	28	(	(	PUNCT
ejpam-5711	334	29	5	5	NUM
ejpam-5711	334	30	n−2)−	n−2)−	VERB
ejpam-5711	334	31	3	3	NUM
ejpam-5711	334	32	4	4	NUM
ejpam-5711	334	33	.	.	PUNCT
ejpam-5711	335	1	(	(	PUNCT
ejpam-5711	335	2	vii	vii	PROPN
ejpam-5711	335	3	)	)	PUNCT
ejpam-5711	335	4	i(fgbn	i(fgbn	NOUN
ejpam-5711	335	5	)	)	PUNCT
ejpam-5711	336	1	=	=	SYM
ejpam-5711	336	2	(	(	PUNCT
ejpam-5711	336	3	sxj)(dxdy(m(fgbn;x	sxj)(dxdy(m(fgbn;x	PROPN
ejpam-5711	336	4	,	,	PUNCT
ejpam-5711	336	5	y)))|x=1	y)))|x=1	X
ejpam-5711	336	6	=	=	NOUN
ejpam-5711	336	7	58(5n−2)−	58(5n−2)−	NUM
ejpam-5711	336	8	6	6	NUM
ejpam-5711	336	9	.	.	PUNCT
ejpam-5711	336	10	remark	remark	NOUN
ejpam-5711	336	11	1	1	NUM
ejpam-5711	336	12	.	.	PUNCT
ejpam-5711	337	1	the	the	DET
ejpam-5711	337	2	order	order	NOUN
ejpam-5711	337	3	and	and	CCONJ
ejpam-5711	337	4	size	size	NOUN
ejpam-5711	337	5	of	of	ADP
ejpam-5711	337	6	all	all	DET
ejpam-5711	337	7	graphs	graph	NOUN
ejpam-5711	337	8	is	be	AUX
ejpam-5711	337	9	given	give	VERB
ejpam-5711	337	10	by	by	ADP
ejpam-5711	337	11	geometric	geometric	ADJ
ejpam-5711	337	12	series	series	NOUN
ejpam-5711	337	13	.	.	PUNCT
ejpam-5711	338	1	2.4	2.4	NUM
ejpam-5711	338	2	.	.	PUNCT
ejpam-5711	338	3	plotting	plot	VERB
ejpam-5711	338	4	representation	representation	NOUN
ejpam-5711	338	5	our	our	PRON
ejpam-5711	338	6	figures	figure	NOUN
ejpam-5711	338	7	2d	2d	NOUN
ejpam-5711	338	8	and	and	CCONJ
ejpam-5711	338	9	3d	3d	NUM
ejpam-5711	338	10	of	of	ADP
ejpam-5711	338	11	m	m	NOUN
ejpam-5711	338	12	-	-	PUNCT
ejpam-5711	338	13	polynomials	polynomial	NOUN
ejpam-5711	338	14	and	and	CCONJ
ejpam-5711	338	15	topological	topological	ADJ
ejpam-5711	338	16	indices	index	NOUN
ejpam-5711	338	17	are	be	AUX
ejpam-5711	338	18	obtained	obtain	VERB
ejpam-5711	338	19	by	by	ADP
ejpam-5711	338	20	wolfram	wolfram	PROPN
ejpam-5711	338	21	mathematica	mathematica	PROPN
ejpam-5711	338	22	.	.	PUNCT
ejpam-5711	339	1	figure	figure	VERB
ejpam-5711	339	2	4	4	NUM
ejpam-5711	339	3	:	:	PUNCT
ejpam-5711	339	4	a	a	DET
ejpam-5711	339	5	3d	3d	NOUN
ejpam-5711	339	6	representation	representation	NOUN
ejpam-5711	339	7	of	of	ADP
ejpam-5711	339	8	the	the	DET
ejpam-5711	339	9	m	m	NOUN
ejpam-5711	339	10	-	-	ADJ
ejpam-5711	339	11	polynomial	polynomial	ADJ
ejpam-5711	339	12	for	for	ADP
ejpam-5711	339	13	benzene	benzene	NOUN
ejpam-5711	339	14	’s	’s	PART
ejpam-5711	339	15	fractal	fractal	ADJ
ejpam-5711	339	16	growth	growth	NOUN
ejpam-5711	339	17	with	with	ADP
ejpam-5711	339	18	n=2,3	n=2,3	PROPN
ejpam-5711	339	19	and	and	CCONJ
ejpam-5711	339	20	4	4	NUM
ejpam-5711	339	21	.	.	PUNCT
ejpam-5711	340	1	-2	-2	INTJ
ejpam-5711	341	1	-1	-1	NOUN
ejpam-5711	341	2	1	1	NUM
ejpam-5711	341	3	2	2	NUM
ejpam-5711	341	4	3	3	NUM
ejpam-5711	341	5	50	50	NUM
ejpam-5711	341	6	100	100	NUM
ejpam-5711	341	7	150	150	NUM
ejpam-5711	341	8	200	200	NUM
ejpam-5711	341	9	figure	figure	NOUN
ejpam-5711	341	10	5	5	NUM
ejpam-5711	341	11	:	:	PUNCT
ejpam-5711	341	12	a	a	DET
ejpam-5711	341	13	2d	2d	NUM
ejpam-5711	341	14	representation	representation	NOUN
ejpam-5711	341	15	of	of	ADP
ejpam-5711	341	16	degree	degree	NOUN
ejpam-5711	341	17	-	-	PUNCT
ejpam-5711	341	18	based	base	VERB
ejpam-5711	341	19	topological	topological	ADJ
ejpam-5711	341	20	indices	index	NOUN
ejpam-5711	341	21	derived	derive	VERB
ejpam-5711	341	22	from	from	ADP
ejpam-5711	341	23	the	the	DET
ejpam-5711	341	24	m	m	NOUN
ejpam-5711	341	25	-	-	ADJ
ejpam-5711	341	26	polynomial	polynomial	ADJ
ejpam-5711	341	27	of	of	ADP
ejpam-5711	341	28	benzene	benzene	NOUN
ejpam-5711	341	29	’s	’s	PART
ejpam-5711	341	30	fractal	fractal	ADJ
ejpam-5711	341	31	growth	growth	NOUN
ejpam-5711	341	32	.	.	PUNCT
ejpam-5711	342	1	n.	n.	PROPN
ejpam-5711	342	2	t.	t.	PROPN
ejpam-5711	342	3	sarhan	sarhan	PROPN
ejpam-5711	342	4	,	,	PUNCT
ejpam-5711	342	5	d.	d.	PROPN
ejpam-5711	342	6	a.	a.	PROPN
ejpam-5711	342	7	ali	ali	PROPN
ejpam-5711	342	8	,	,	PUNCT
ejpam-5711	342	9	g.	g.	PROPN
ejpam-5711	342	10	h.	h.	PROPN
ejpam-5711	343	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	343	2	/	/	SYM
ejpam-5711	343	3	eur	eur	PROPN
ejpam-5711	343	4	.	.	PUNCT
ejpam-5711	344	1	j.	j.	PROPN
ejpam-5711	344	2	pure	pure	PROPN
ejpam-5711	344	3	appl	appl	PROPN
ejpam-5711	344	4	.	.	PROPN
ejpam-5711	344	5	math	math	PROPN
ejpam-5711	344	6	,	,	PUNCT
ejpam-5711	344	7	18	18	NUM
ejpam-5711	344	8	(	(	PUNCT
ejpam-5711	344	9	1	1	NUM
ejpam-5711	344	10	)	)	PUNCT
ejpam-5711	344	11	(	(	PUNCT
ejpam-5711	344	12	2025	2025	NUM
ejpam-5711	344	13	)	)	PUNCT
ejpam-5711	344	14	,	,	PUNCT
ejpam-5711	344	15	5711	5711	NUM
ejpam-5711	344	16	12	12	NUM
ejpam-5711	344	17	of	of	ADP
ejpam-5711	344	18	15	15	NUM
ejpam-5711	344	19	figure	figure	NOUN
ejpam-5711	344	20	6	6	NUM
ejpam-5711	344	21	:	:	PUNCT
ejpam-5711	344	22	a	a	DET
ejpam-5711	344	23	3d	3d	NOUN
ejpam-5711	344	24	representation	representation	NOUN
ejpam-5711	344	25	of	of	ADP
ejpam-5711	344	26	the	the	DET
ejpam-5711	344	27	m	m	NOUN
ejpam-5711	344	28	-	-	NOUN
ejpam-5711	344	29	polynomial	polynomial	ADJ
ejpam-5711	344	30	for	for	ADP
ejpam-5711	344	31	a	a	DET
ejpam-5711	344	32	pythagoras	pythagoras	PROPN
ejpam-5711	344	33	tree	tree	NOUN
ejpam-5711	344	34	with	with	ADP
ejpam-5711	344	35	n=2,3	n=2,3	PROPN
ejpam-5711	344	36	and	and	CCONJ
ejpam-5711	344	37	4	4	NUM
ejpam-5711	344	38	.	.	PUNCT
ejpam-5711	344	39	-2	-2	NOUN
ejpam-5711	345	1	2	2	NUM
ejpam-5711	345	2	4	4	NUM
ejpam-5711	345	3	6	6	NUM
ejpam-5711	345	4	8	8	NUM
ejpam-5711	345	5	10	10	NUM
ejpam-5711	345	6	2000	2000	NUM
ejpam-5711	345	7	4000	4000	NUM
ejpam-5711	345	8	6000	6000	NUM
ejpam-5711	345	9	8000	8000	NUM
ejpam-5711	345	10	10000	10000	NUM
ejpam-5711	345	11	12000	12000	NUM
ejpam-5711	345	12	14000	14000	NUM
ejpam-5711	345	13	figure	figure	NOUN
ejpam-5711	345	14	7	7	NUM
ejpam-5711	345	15	:	:	PUNCT
ejpam-5711	345	16	a	a	DET
ejpam-5711	345	17	2d	2d	NUM
ejpam-5711	345	18	representation	representation	NOUN
ejpam-5711	345	19	of	of	ADP
ejpam-5711	345	20	degree	degree	NOUN
ejpam-5711	345	21	-	-	PUNCT
ejpam-5711	345	22	based	base	VERB
ejpam-5711	345	23	topological	topological	ADJ
ejpam-5711	345	24	indices	index	NOUN
ejpam-5711	345	25	derived	derive	VERB
ejpam-5711	345	26	from	from	ADP
ejpam-5711	345	27	the	the	DET
ejpam-5711	345	28	m	m	NOUN
ejpam-5711	345	29	-	-	NOUN
ejpam-5711	345	30	polynomial	polynomial	ADJ
ejpam-5711	345	31	of	of	ADP
ejpam-5711	345	32	a	a	DET
ejpam-5711	345	33	pythagoras	pythagoras	PROPN
ejpam-5711	345	34	tree	tree	NOUN
ejpam-5711	345	35	.	.	PUNCT
ejpam-5711	346	1	figure	figure	VERB
ejpam-5711	346	2	8	8	NUM
ejpam-5711	346	3	:	:	PUNCT
ejpam-5711	346	4	a	a	DET
ejpam-5711	346	5	3d	3d	NOUN
ejpam-5711	346	6	representation	representation	NOUN
ejpam-5711	346	7	of	of	ADP
ejpam-5711	346	8	the	the	DET
ejpam-5711	346	9	m	m	NOUN
ejpam-5711	346	10	-	-	NOUN
ejpam-5711	346	11	polynomial	polynomial	ADJ
ejpam-5711	346	12	for	for	ADP
ejpam-5711	346	13	a	a	DET
ejpam-5711	346	14	benzene	benzene	NOUN
ejpam-5711	346	15	dendrimer	dendrimer	NOUN
ejpam-5711	346	16	with	with	ADP
ejpam-5711	346	17	n=2,3	n=2,3	PROPN
ejpam-5711	346	18	and	and	CCONJ
ejpam-5711	346	19	4	4	NUM
ejpam-5711	346	20	.	.	PUNCT
ejpam-5711	346	21	n.	n.	PROPN
ejpam-5711	346	22	t.	t.	PROPN
ejpam-5711	346	23	sarhan	sarhan	PROPN
ejpam-5711	346	24	,	,	PUNCT
ejpam-5711	346	25	d.	d.	PROPN
ejpam-5711	346	26	a.	a.	PROPN
ejpam-5711	346	27	ali	ali	PROPN
ejpam-5711	346	28	,	,	PUNCT
ejpam-5711	347	1	g.	g.	PROPN
ejpam-5711	347	2	h.	h.	PROPN
ejpam-5711	347	3	mohiaddin	mohiaddin	PROPN
ejpam-5711	347	4	/	/	SYM
ejpam-5711	347	5	eur	eur	PROPN
ejpam-5711	347	6	.	.	PUNCT
ejpam-5711	348	1	j.	j.	PROPN
ejpam-5711	348	2	pure	pure	PROPN
ejpam-5711	348	3	appl	appl	PROPN
ejpam-5711	348	4	.	.	PROPN
ejpam-5711	348	5	math	math	PROPN
ejpam-5711	348	6	,	,	PUNCT
ejpam-5711	348	7	18	18	NUM
ejpam-5711	348	8	(	(	PUNCT
ejpam-5711	348	9	1	1	NUM
ejpam-5711	348	10	)	)	PUNCT
ejpam-5711	348	11	(	(	PUNCT
ejpam-5711	348	12	2025	2025	NUM
ejpam-5711	348	13	)	)	PUNCT
ejpam-5711	348	14	,	,	PUNCT
ejpam-5711	348	15	5711	5711	NUM
ejpam-5711	348	16	13	13	NUM
ejpam-5711	348	17	of	of	ADP
ejpam-5711	348	18	15	15	NUM
ejpam-5711	348	19	-2	-2	NOUN
ejpam-5711	348	20	-1	-1	NOUN
ejpam-5711	348	21	1	1	NUM
ejpam-5711	348	22	2	2	NUM
ejpam-5711	348	23	3	3	NUM
ejpam-5711	348	24	-50	-50	PUNCT
ejpam-5711	348	25	50	50	NUM
ejpam-5711	348	26	100	100	NUM
ejpam-5711	348	27	150	150	NUM
ejpam-5711	348	28	200	200	NUM
ejpam-5711	348	29	figure	figure	NOUN
ejpam-5711	348	30	9	9	NUM
ejpam-5711	348	31	:	:	PUNCT
ejpam-5711	348	32	a	a	DET
ejpam-5711	348	33	2d	2d	NUM
ejpam-5711	348	34	representation	representation	NOUN
ejpam-5711	348	35	of	of	ADP
ejpam-5711	348	36	degree	degree	NOUN
ejpam-5711	348	37	-	-	PUNCT
ejpam-5711	348	38	based	base	VERB
ejpam-5711	348	39	topological	topological	ADJ
ejpam-5711	348	40	indices	index	NOUN
ejpam-5711	348	41	derived	derive	VERB
ejpam-5711	348	42	from	from	ADP
ejpam-5711	348	43	the	the	DET
ejpam-5711	348	44	m	m	NOUN
ejpam-5711	348	45	-	-	ADJ
ejpam-5711	348	46	polynomial	polynomial	ADJ
ejpam-5711	348	47	of	of	ADP
ejpam-5711	348	48	a	a	DET
ejpam-5711	348	49	benzene	benzene	NOUN
ejpam-5711	348	50	dendrimer	dendrimer	NOUN
ejpam-5711	348	51	.	.	PUNCT
ejpam-5711	349	1	figure	figure	VERB
ejpam-5711	349	2	10	10	NUM
ejpam-5711	349	3	:	:	PUNCT
ejpam-5711	349	4	a	a	DET
ejpam-5711	349	5	3d	3d	NOUN
ejpam-5711	349	6	representation	representation	NOUN
ejpam-5711	349	7	of	of	ADP
ejpam-5711	349	8	the	the	DET
ejpam-5711	349	9	general	general	PROPN
ejpam-5711	349	10	randic	randic	ADJ
ejpam-5711	349	11	index	index	NOUN
ejpam-5711	349	12	for	for	ADP
ejpam-5711	349	13	above	above	ADV
ejpam-5711	349	14	three	three	NUM
ejpam-5711	349	15	graphs	graph	NOUN
ejpam-5711	349	16	with	with	ADP
ejpam-5711	349	17	n=3,6	n=3,6	PROPN
ejpam-5711	349	18	and	and	CCONJ
ejpam-5711	349	19	γ=1,2	γ=1,2	PROPN
ejpam-5711	349	20	3	3	NUM
ejpam-5711	349	21	.	.	PUNCT
ejpam-5711	350	1	conclusions	conclusion	NOUN
ejpam-5711	350	2	in	in	ADP
ejpam-5711	350	3	this	this	DET
ejpam-5711	350	4	article	article	NOUN
ejpam-5711	350	5	,	,	PUNCT
ejpam-5711	350	6	we	we	PRON
ejpam-5711	350	7	have	have	AUX
ejpam-5711	350	8	derived	derive	VERB
ejpam-5711	350	9	the	the	DET
ejpam-5711	350	10	general	general	ADJ
ejpam-5711	350	11	forms	form	NOUN
ejpam-5711	350	12	of	of	ADP
ejpam-5711	350	13	the	the	DET
ejpam-5711	350	14	m	m	NOUN
ejpam-5711	350	15	-	-	PUNCT
ejpam-5711	350	16	polynomials	polynomial	NOUN
ejpam-5711	350	17	for	for	ADP
ejpam-5711	350	18	the	the	DET
ejpam-5711	350	19	fractal	fractal	ADJ
ejpam-5711	350	20	growth	growth	NOUN
ejpam-5711	350	21	patterns	pattern	NOUN
ejpam-5711	350	22	of	of	ADP
ejpam-5711	350	23	benzene	benzene	NOUN
ejpam-5711	350	24	(	(	PUNCT
ejpam-5711	350	25	fgbn	fgbn	NOUN
ejpam-5711	350	26	,	,	PUNCT
ejpam-5711	350	27	n	n	X
ejpam-5711	350	28	≥	≥	NOUN
ejpam-5711	350	29	1	1	NUM
ejpam-5711	350	30	)	)	PUNCT
ejpam-5711	350	31	,	,	PUNCT
ejpam-5711	350	32	the	the	DET
ejpam-5711	350	33	pythagoras	pythagoras	PROPN
ejpam-5711	350	34	tree	tree	NOUN
ejpam-5711	350	35	(	(	PUNCT
ejpam-5711	350	36	ptn	ptn	PROPN
ejpam-5711	350	37	,	,	PUNCT
ejpam-5711	350	38	n	n	PRON
ejpam-5711	350	39	≥	≥	NOUN
ejpam-5711	350	40	1	1	NUM
ejpam-5711	350	41	)	)	PUNCT
ejpam-5711	350	42	,	,	PUNCT
ejpam-5711	350	43	and	and	CCONJ
ejpam-5711	350	44	the	the	DET
ejpam-5711	350	45	benzene	benzene	NOUN
ejpam-5711	350	46	dendrimer	dendrimer	NOUN
ejpam-5711	350	47	(	(	PUNCT
ejpam-5711	350	48	dbn	dbn	PROPN
ejpam-5711	350	49	,	,	PUNCT
ejpam-5711	350	50	n	n	PRON
ejpam-5711	350	51	≥	≥	NOUN
ejpam-5711	350	52	2	2	NUM
ejpam-5711	350	53	)	)	PUNCT
ejpam-5711	350	54	.	.	PUNCT
ejpam-5711	351	1	additionally	additionally	ADV
ejpam-5711	351	2	,	,	PUNCT
ejpam-5711	351	3	we	we	PRON
ejpam-5711	351	4	computed	compute	VERB
ejpam-5711	351	5	degree	degree	NOUN
ejpam-5711	351	6	-	-	PUNCT
ejpam-5711	351	7	based	base	VERB
ejpam-5711	351	8	topological	topological	ADJ
ejpam-5711	351	9	indices	index	NOUN
ejpam-5711	351	10	associated	associate	VERB
ejpam-5711	351	11	with	with	ADP
ejpam-5711	351	12	these	these	DET
ejpam-5711	351	13	polynomials	polynomial	NOUN
ejpam-5711	351	14	.	.	PUNCT
ejpam-5711	352	1	the	the	DET
ejpam-5711	352	2	graphical	graphical	ADJ
ejpam-5711	352	3	representations	representation	NOUN
ejpam-5711	352	4	in	in	ADP
ejpam-5711	352	5	figures	figure	NOUN
ejpam-5711	352	6	(	(	PUNCT
ejpam-5711	352	7	4	4	NUM
ejpam-5711	352	8	,	,	PUNCT
ejpam-5711	352	9	6	6	NUM
ejpam-5711	352	10	,	,	PUNCT
ejpam-5711	352	11	8)	8)	NUM
ejpam-5711	352	12	illustrate	illustrate	VERB
ejpam-5711	352	13	the	the	DET
ejpam-5711	352	14	m	m	ADJ
ejpam-5711	352	15	-	-	ADJ
ejpam-5711	352	16	polynomial	polynomial	ADJ
ejpam-5711	352	17	graphs	graph	NOUN
ejpam-5711	352	18	for	for	ADP
ejpam-5711	352	19	the	the	DET
ejpam-5711	352	20	fractal	fractal	ADJ
ejpam-5711	352	21	growth	growth	NOUN
ejpam-5711	352	22	patterns	pattern	NOUN
ejpam-5711	352	23	of	of	ADP
ejpam-5711	352	24	benzene	benzene	NOUN
ejpam-5711	352	25	fgbn	fgbn	NOUN
ejpam-5711	352	26	,	,	PUNCT
ejpam-5711	352	27	the	the	DET
ejpam-5711	352	28	pythagoras	pythagoras	PROPN
ejpam-5711	352	29	tree	tree	NOUN
ejpam-5711	352	30	ptn	ptn	PROPN
ejpam-5711	352	31	,	,	PUNCT
ejpam-5711	352	32	and	and	CCONJ
ejpam-5711	352	33	the	the	DET
ejpam-5711	352	34	benzene	benzene	NOUN
ejpam-5711	352	35	dendrimer	dendrimer	PROPN
ejpam-5711	352	36	dbn	dbn	PROPN
ejpam-5711	352	37	for	for	ADP
ejpam-5711	352	38	n	n	NOUN
ejpam-5711	352	39	=	=	SYM
ejpam-5711	352	40	2	2	NUM
ejpam-5711	352	41	,	,	PUNCT
ejpam-5711	352	42	3	3	NUM
ejpam-5711	352	43	,	,	PUNCT
ejpam-5711	352	44	4	4	NUM
ejpam-5711	352	45	.	.	PUNCT
ejpam-5711	353	1	it	it	PRON
ejpam-5711	353	2	is	be	AUX
ejpam-5711	353	3	evident	evident	ADJ
ejpam-5711	353	4	that	that	SCONJ
ejpam-5711	353	5	as	as	ADP
ejpam-5711	353	6	n	n	DET
ejpam-5711	353	7	increases	increase	NOUN
ejpam-5711	353	8	,	,	PUNCT
ejpam-5711	353	9	the	the	DET
ejpam-5711	353	10	graph	graph	NOUN
ejpam-5711	353	11	in	in	ADP
ejpam-5711	353	12	figure	figure	NOUN
ejpam-5711	353	13	4	4	NUM
ejpam-5711	353	14	becomes	become	VERB
ejpam-5711	353	15	larger	large	ADJ
ejpam-5711	353	16	than	than	ADP
ejpam-5711	353	17	that	that	PRON
ejpam-5711	353	18	in	in	ADP
ejpam-5711	353	19	figure	figure	NOUN
ejpam-5711	353	20	8	8	NUM
ejpam-5711	353	21	,	,	PUNCT
ejpam-5711	353	22	and	and	CCONJ
ejpam-5711	353	23	both	both	PRON
ejpam-5711	353	24	surpass	surpass	VERB
ejpam-5711	353	25	the	the	DET
ejpam-5711	353	26	graph	graph	NOUN
ejpam-5711	353	27	in	in	ADP
ejpam-5711	353	28	figure	figure	NOUN
ejpam-5711	353	29	8	8	NUM
ejpam-5711	353	30	.	.	PUNCT
ejpam-5711	354	1	similarly	similarly	ADV
ejpam-5711	354	2	,	,	PUNCT
ejpam-5711	354	3	the	the	DET
ejpam-5711	354	4	topological	topological	ADJ
ejpam-5711	354	5	indices	index	NOUN
ejpam-5711	354	6	shown	show	VERB
ejpam-5711	354	7	in	in	ADP
ejpam-5711	354	8	figure	figure	NOUN
ejpam-5711	354	9	5	5	NUM
ejpam-5711	354	10	are	be	AUX
ejpam-5711	354	11	greater	great	ADJ
ejpam-5711	354	12	than	than	ADP
ejpam-5711	354	13	those	those	PRON
ejpam-5711	354	14	in	in	ADP
ejpam-5711	354	15	figure	figure	NOUN
ejpam-5711	354	16	7	7	NUM
ejpam-5711	354	17	,	,	PUNCT
ejpam-5711	354	18	which	which	PRON
ejpam-5711	354	19	in	in	ADP
ejpam-5711	354	20	turn	turn	NOUN
ejpam-5711	354	21	are	be	AUX
ejpam-5711	354	22	larger	large	ADJ
ejpam-5711	354	23	than	than	ADP
ejpam-5711	354	24	those	those	PRON
ejpam-5711	354	25	in	in	ADP
ejpam-5711	354	26	figure	figure	NOUN
ejpam-5711	354	27	9	9	NUM
ejpam-5711	354	28	.	.	PUNCT
ejpam-5711	355	1	these	these	DET
ejpam-5711	355	2	findings	finding	NOUN
ejpam-5711	355	3	highlight	highlight	VERB
ejpam-5711	355	4	the	the	DET
ejpam-5711	355	5	trends	trend	NOUN
ejpam-5711	355	6	in	in	ADP
ejpam-5711	355	7	graph	graph	NOUN
ejpam-5711	355	8	growth	growth	NOUN
ejpam-5711	355	9	and	and	CCONJ
ejpam-5711	355	10	the	the	DET
ejpam-5711	355	11	corresponding	corresponding	ADJ
ejpam-5711	355	12	indices	index	NOUN
ejpam-5711	355	13	as	as	SCONJ
ejpam-5711	355	14	the	the	DET
ejpam-5711	355	15	fractal	fractal	ADJ
ejpam-5711	355	16	structure	structure	NOUN
ejpam-5711	355	17	evolves	evolve	VERB
ejpam-5711	355	18	.	.	PUNCT
ejpam-5711	356	1	n.	n.	PROPN
ejpam-5711	356	2	t.	t.	PROPN
ejpam-5711	356	3	sarhan	sarhan	PROPN
ejpam-5711	356	4	,	,	PUNCT
ejpam-5711	356	5	d.	d.	PROPN
ejpam-5711	356	6	a.	a.	PROPN
ejpam-5711	356	7	ali	ali	PROPN
ejpam-5711	356	8	,	,	PUNCT
ejpam-5711	356	9	g.	g.	PROPN
ejpam-5711	356	10	h.	h.	PROPN
ejpam-5711	357	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	357	2	/	/	SYM
ejpam-5711	357	3	eur	eur	PROPN
ejpam-5711	357	4	.	.	PUNCT
ejpam-5711	358	1	j.	j.	PROPN
ejpam-5711	358	2	pure	pure	PROPN
ejpam-5711	358	3	appl	appl	PROPN
ejpam-5711	358	4	.	.	PROPN
ejpam-5711	358	5	math	math	PROPN
ejpam-5711	358	6	,	,	PUNCT
ejpam-5711	358	7	18	18	NUM
ejpam-5711	358	8	(	(	PUNCT
ejpam-5711	358	9	1	1	NUM
ejpam-5711	358	10	)	)	PUNCT
ejpam-5711	358	11	(	(	PUNCT
ejpam-5711	358	12	2025	2025	NUM
ejpam-5711	358	13	)	)	PUNCT
ejpam-5711	358	14	,	,	PUNCT
ejpam-5711	358	15	5711	5711	NUM
ejpam-5711	358	16	14	14	NUM
ejpam-5711	358	17	of	of	ADP
ejpam-5711	358	18	15	15	NUM
ejpam-5711	358	19	references	reference	NOUN
ejpam-5711	358	20	[	[	X
ejpam-5711	358	21	1	1	NUM
ejpam-5711	358	22	]	]	PUNCT
ejpam-5711	358	23	a.	a.	PROPN
ejpam-5711	358	24	ali	ali	PROPN
ejpam-5711	358	25	,	,	PUNCT
ejpam-5711	358	26	w.	w.	PROPN
ejpam-5711	358	27	nazeer	nazeer	PROPN
ejpam-5711	358	28	,	,	PUNCT
ejpam-5711	358	29	m.	m.	PROPN
ejpam-5711	358	30	munir	munir	PROPN
ejpam-5711	358	31	,	,	PUNCT
ejpam-5711	358	32	and	and	CCONJ
ejpam-5711	358	33	s.	s.	PROPN
ejpam-5711	358	34	m.	m.	PROPN
ejpam-5711	358	35	kan	kan	PROPN
ejpam-5711	358	36	.	.	PUNCT
ejpam-5711	359	1	m	m	NOUN
ejpam-5711	359	2	-	-	PUNCT
ejpam-5711	359	3	polynomials	polynomial	NOUN
ejpam-5711	359	4	and	and	CCONJ
ejpam-5711	359	5	topological	topological	ADJ
ejpam-5711	359	6	indices	index	NOUN
ejpam-5711	359	7	of	of	ADP
ejpam-5711	359	8	zigzag	zigzag	NOUN
ejpam-5711	359	9	and	and	CCONJ
ejpam-5711	359	10	rhombic	rhombic	ADJ
ejpam-5711	359	11	benzenoid	benzenoid	NOUN
ejpam-5711	359	12	systems	system	NOUN
ejpam-5711	359	13	.	.	PUNCT
ejpam-5711	360	1	open	open	ADJ
ejpam-5711	360	2	chemistry	chemistry	NOUN
ejpam-5711	360	3	,	,	PUNCT
ejpam-5711	360	4	16(1):73–78	16(1):73–78	NUM
ejpam-5711	360	5	,	,	PUNCT
ejpam-5711	360	6	2018	2018	NUM
ejpam-5711	360	7	.	.	PUNCT
ejpam-5711	361	1	[	[	X
ejpam-5711	361	2	2	2	X
ejpam-5711	361	3	]	]	PUNCT
ejpam-5711	361	4	d.	d.	PROPN
ejpam-5711	361	5	a.	a.	PROPN
ejpam-5711	361	6	ali	ali	PROPN
ejpam-5711	361	7	,	,	PUNCT
ejpam-5711	361	8	h.	h.	PROPN
ejpam-5711	361	9	ali	ali	PROPN
ejpam-5711	361	10	,	,	PUNCT
ejpam-5711	361	11	q.	q.	PROPN
ejpam-5711	361	12	u.	u.	PROPN
ejpam-5711	361	13	ain	ain	PROPN
ejpam-5711	361	14	,	,	PUNCT
ejpam-5711	361	15	s.	s.	PROPN
ejpam-5711	361	16	a.	a.	PROPN
ejpam-5711	361	17	k.	k.	PROPN
ejpam-5711	361	18	kirmani	kirmani	PROPN
ejpam-5711	361	19	,	,	PUNCT
ejpam-5711	361	20	p.	p.	NOUN
ejpam-5711	361	21	a.	a.	NOUN
ejpam-5711	361	22	,	,	PUNCT
ejpam-5711	361	23	and	and	CCONJ
ejpam-5711	361	24	m.	m.	NOUN
ejpam-5711	361	25	sesay	sesay	PROPN
ejpam-5711	361	26	.	.	PUNCT
ejpam-5711	362	1	computation	computation	NOUN
ejpam-5711	362	2	of	of	ADP
ejpam-5711	362	3	benzenoid	benzenoid	NOUN
ejpam-5711	362	4	planar	planar	ADJ
ejpam-5711	362	5	octahedron	octahedron	NOUN
ejpam-5711	362	6	networks	network	NOUN
ejpam-5711	362	7	by	by	ADP
ejpam-5711	362	8	using	use	VERB
ejpam-5711	362	9	topological	topological	ADJ
ejpam-5711	362	10	indices	index	NOUN
ejpam-5711	362	11	.	.	PUNCT
ejpam-5711	363	1	mathematical	mathematical	ADJ
ejpam-5711	363	2	problems	problem	NOUN
ejpam-5711	363	3	in	in	ADP
ejpam-5711	363	4	engineering	engineering	NOUN
ejpam-5711	363	5	,	,	PUNCT
ejpam-5711	363	6	2023(1):2686873	2023(1):2686873	ADP
ejpam-5711	363	7	,	,	PUNCT
ejpam-5711	363	8	2023	2023	NUM
ejpam-5711	363	9	.	.	PUNCT
ejpam-5711	364	1	[	[	X
ejpam-5711	364	2	3	3	X
ejpam-5711	364	3	]	]	X
ejpam-5711	364	4	h.	h.	PROPN
ejpam-5711	364	5	ali	ali	PROPN
ejpam-5711	364	6	,	,	PUNCT
ejpam-5711	364	7	d.	d.	PROPN
ejpam-5711	364	8	a.	a.	PROPN
ejpam-5711	364	9	ali	ali	PROPN
ejpam-5711	364	10	,	,	PUNCT
ejpam-5711	364	11	f.	f.	PROPN
ejpam-5711	364	12	liaqat	liaqat	PROPN
ejpam-5711	364	13	,	,	PUNCT
ejpam-5711	364	14	m.	m.	NOUN
ejpam-5711	364	15	h.	h.	PROPN
ejpam-5711	364	16	yaseen	yaseen	PROPN
ejpam-5711	364	17	,	,	PUNCT
ejpam-5711	364	18	m.	m.	PROPN
ejpam-5711	364	19	i.	i.	PROPN
ejpam-5711	364	20	khan	khan	PROPN
ejpam-5711	364	21	,	,	PUNCT
ejpam-5711	364	22	s.	s.	PROPN
ejpam-5711	364	23	ali	ali	PROPN
ejpam-5711	364	24	,	,	PUNCT
ejpam-5711	364	25	n.	n.	PROPN
ejpam-5711	364	26	almalki	almalki	ADV
ejpam-5711	364	27	,	,	PUNCT
ejpam-5711	364	28	and	and	CCONJ
ejpam-5711	364	29	b.	b.	PROPN
ejpam-5711	364	30	s.	s.	PROPN
ejpam-5711	364	31	abdullaeva	abdullaeva	PROPN
ejpam-5711	364	32	.	.	PUNCT
ejpam-5711	365	1	on	on	ADP
ejpam-5711	365	2	topological	topological	ADJ
ejpam-5711	365	3	indices	index	NOUN
ejpam-5711	365	4	of	of	ADP
ejpam-5711	365	5	third	third	ADJ
ejpam-5711	365	6	types	type	NOUN
ejpam-5711	365	7	of	of	ADP
ejpam-5711	365	8	hex	hex	NOUN
ejpam-5711	365	9	-	-	PUNCT
ejpam-5711	365	10	derived	derive	VERB
ejpam-5711	365	11	networks	network	NOUN
ejpam-5711	365	12	.	.	PUNCT
ejpam-5711	366	1	journal	journal	PROPN
ejpam-5711	366	2	of	of	ADP
ejpam-5711	366	3	mathematical	mathematical	ADJ
ejpam-5711	366	4	chemistry	chemistry	NOUN
ejpam-5711	366	5	,	,	PUNCT
ejpam-5711	366	6	62:2407–2429	62:2407–2429	NUM
ejpam-5711	366	7	,	,	PUNCT
ejpam-5711	366	8	2024	2024	NUM
ejpam-5711	366	9	.	.	PUNCT
ejpam-5711	367	1	[	[	X
ejpam-5711	367	2	4	4	X
ejpam-5711	367	3	]	]	PUNCT
ejpam-5711	367	4	k.	k.	PROPN
ejpam-5711	367	5	k.	k.	PROPN
ejpam-5711	367	6	ali	ali	PROPN
ejpam-5711	367	7	,	,	PUNCT
ejpam-5711	367	8	a.	a.	PROPN
ejpam-5711	367	9	k.	k.	PROPN
ejpam-5711	367	10	golmankhaneh	golmankhaneh	PROPN
ejpam-5711	367	11	,	,	PUNCT
ejpam-5711	367	12	and	and	CCONJ
ejpam-5711	367	13	r.	r.	PROPN
ejpam-5711	367	14	yilmazer	yilmazer	PROPN
ejpam-5711	367	15	.	.	PUNCT
ejpam-5711	368	1	battery	battery	NOUN
ejpam-5711	368	2	discharging	discharge	VERB
ejpam-5711	368	3	model	model	NOUN
ejpam-5711	368	4	on	on	ADP
ejpam-5711	368	5	fractal	fractal	ADJ
ejpam-5711	368	6	time	time	NOUN
ejpam-5711	368	7	sets	set	NOUN
ejpam-5711	368	8	.	.	PUNCT
ejpam-5711	369	1	international	international	ADJ
ejpam-5711	369	2	journal	journal	PROPN
ejpam-5711	369	3	of	of	ADP
ejpam-5711	369	4	nonlinear	nonlinear	PROPN
ejpam-5711	369	5	sciences	sciences	PROPN
ejpam-5711	369	6	and	and	CCONJ
ejpam-5711	369	7	numerical	numerical	PROPN
ejpam-5711	369	8	simulation	simulation	NOUN
ejpam-5711	369	9	,	,	PUNCT
ejpam-5711	369	10	24(1):71–80	24(1):71–80	NUM
ejpam-5711	369	11	,	,	PUNCT
ejpam-5711	369	12	2023	2023	NUM
ejpam-5711	369	13	.	.	PUNCT
ejpam-5711	370	1	[	[	X
ejpam-5711	370	2	5	5	X
ejpam-5711	370	3	]	]	X
ejpam-5711	370	4	b.	b.	PROPN
ejpam-5711	370	5	bollobas	bollobas	PROPN
ejpam-5711	370	6	and	and	CCONJ
ejpam-5711	370	7	p.	p.	NOUN
ejpam-5711	370	8	erdos	erdo	NOUN
ejpam-5711	370	9	.	.	PUNCT
ejpam-5711	371	1	graphs	graph	NOUN
ejpam-5711	371	2	of	of	ADP
ejpam-5711	371	3	extremal	extremal	ADJ
ejpam-5711	371	4	weights	weight	NOUN
ejpam-5711	371	5	.	.	PUNCT
ejpam-5711	372	1	ars	ars	PROPN
ejpam-5711	372	2	combinatoria	combinatoria	PROPN
ejpam-5711	372	3	,	,	PUNCT
ejpam-5711	372	4	50:225	50:225	NUM
ejpam-5711	372	5	–	–	PUNCT
ejpam-5711	372	6	233	233	NUM
ejpam-5711	372	7	,	,	PUNCT
ejpam-5711	372	8	1998	1998	NUM
ejpam-5711	372	9	.	.	PUNCT
ejpam-5711	373	1	[	[	X
ejpam-5711	373	2	6	6	NUM
ejpam-5711	373	3	]	]	PUNCT
ejpam-5711	373	4	e.	e.	PROPN
ejpam-5711	373	5	deutsch	deutsch	PROPN
ejpam-5711	373	6	and	and	CCONJ
ejpam-5711	373	7	s.	s.	PROPN
ejpam-5711	373	8	klavzar	klavzar	PROPN
ejpam-5711	373	9	.	.	PUNCT
ejpam-5711	374	1	m	m	PROPN
ejpam-5711	374	2	-	-	ADJ
ejpam-5711	374	3	polynomial	polynomial	ADJ
ejpam-5711	374	4	and	and	CCONJ
ejpam-5711	374	5	degree	degree	NOUN
ejpam-5711	374	6	-	-	PUNCT
ejpam-5711	374	7	based	base	VERB
ejpam-5711	374	8	topological	topological	ADJ
ejpam-5711	374	9	indices	index	NOUN
ejpam-5711	374	10	.	.	PUNCT
ejpam-5711	375	1	iranian	iranian	ADJ
ejpam-5711	375	2	journal	journal	PROPN
ejpam-5711	375	3	of	of	ADP
ejpam-5711	375	4	mathematical	mathematical	ADJ
ejpam-5711	375	5	chemistry	chemistry	NOUN
ejpam-5711	375	6	,	,	PUNCT
ejpam-5711	375	7	6(2):93–102	6(2):93–102	NUM
ejpam-5711	375	8	,	,	PUNCT
ejpam-5711	375	9	2015	2015	NUM
ejpam-5711	375	10	.	.	PUNCT
ejpam-5711	376	1	[	[	X
ejpam-5711	376	2	7	7	X
ejpam-5711	376	3	]	]	X
ejpam-5711	376	4	s.	s.	PROPN
ejpam-5711	376	5	fajtlowicz	fajtlowicz	PROPN
ejpam-5711	376	6	.	.	PUNCT
ejpam-5711	377	1	on	on	ADP
ejpam-5711	377	2	conjectures	conjecture	NOUN
ejpam-5711	377	3	of	of	ADP
ejpam-5711	377	4	graffiti	graffiti	NOUN
ejpam-5711	377	5	.	.	PUNCT
ejpam-5711	378	1	congressional	congressional	ADJ
ejpam-5711	378	2	number	number	NOUN
ejpam-5711	378	3	,	,	PUNCT
ejpam-5711	378	4	60:187–197	60:187–197	PROPN
ejpam-5711	378	5	,	,	PUNCT
ejpam-5711	378	6	1987	1987	NUM
ejpam-5711	378	7	.	.	PUNCT
ejpam-5711	379	1	[	[	X
ejpam-5711	379	2	8	8	NUM
ejpam-5711	379	3	]	]	X
ejpam-5711	379	4	c.	c.	NOUN
ejpam-5711	379	5	fun	fun	PROPN
ejpam-5711	379	6	,	,	PUNCT
ejpam-5711	379	7	m.	m.	NOUN
ejpam-5711	379	8	munir	munir	PROPN
ejpam-5711	379	9	,	,	PUNCT
ejpam-5711	379	10	z.	z.	PROPN
ejpam-5711	379	11	hussain	hussain	PROPN
ejpam-5711	379	12	,	,	PUNCT
ejpam-5711	379	13	m.	m.	NOUN
ejpam-5711	379	14	athar	athar	PROPN
ejpam-5711	379	15	,	,	PUNCT
ejpam-5711	379	16	and	and	CCONJ
ejpam-5711	379	17	j.	j.	PROPN
ejpam-5711	379	18	b.	b.	PROPN
ejpam-5711	379	19	liu	liu	PROPN
ejpam-5711	379	20	.	.	PUNCT
ejpam-5711	380	1	polynomials	polynomial	NOUN
ejpam-5711	380	2	and	and	CCONJ
ejpam-5711	380	3	general	general	ADJ
ejpam-5711	380	4	degree	degree	NOUN
ejpam-5711	380	5	-	-	PUNCT
ejpam-5711	380	6	based	base	VERB
ejpam-5711	380	7	topological	topological	ADJ
ejpam-5711	380	8	indices	index	NOUN
ejpam-5711	380	9	of	of	ADP
ejpam-5711	380	10	generalized	generalized	ADJ
ejpam-5711	380	11	sierpinski	sierpinski	ADJ
ejpam-5711	380	12	networks	network	NOUN
ejpam-5711	380	13	.	.	PUNCT
ejpam-5711	381	1	complexity	complexity	NOUN
ejpam-5711	381	2	,	,	PUNCT
ejpam-5711	381	3	page	page	NOUN
ejpam-5711	381	4	10	10	NUM
ejpam-5711	381	5	pages	page	NOUN
ejpam-5711	381	6	,	,	PUNCT
ejpam-5711	381	7	2021	2021	NUM
ejpam-5711	381	8	.	.	PUNCT
ejpam-5711	382	1	[	[	X
ejpam-5711	382	2	9	9	NUM
ejpam-5711	382	3	]	]	PUNCT
ejpam-5711	382	4	c.	c.	PROPN
ejpam-5711	382	5	k.	k.	PROPN
ejpam-5711	382	6	gupta	gupta	PROPN
ejpam-5711	382	7	,	,	PUNCT
ejpam-5711	382	8	v.	v.	ADP
ejpam-5711	382	9	lokesha	lokesha	PROPN
ejpam-5711	382	10	,	,	PUNCT
ejpam-5711	382	11	b.	b.	PROPN
ejpam-5711	382	12	s.	s.	PROPN
ejpam-5711	382	13	shetty	shetty	PROPN
ejpam-5711	382	14	,	,	PUNCT
ejpam-5711	382	15	and	and	CCONJ
ejpam-5711	382	16	p.	p.	PROPN
ejpam-5711	382	17	s.	s.	PROPN
ejpam-5711	382	18	rnjini	rnjini	PROPN
ejpam-5711	382	19	.	.	PUNCT
ejpam-5711	383	1	on	on	ADP
ejpam-5711	383	2	the	the	DET
ejpam-5711	383	3	symmetric	symmetric	ADJ
ejpam-5711	383	4	division	division	NOUN
ejpam-5711	383	5	deg	deg	PROPN
ejpam-5711	383	6	index	index	NOUN
ejpam-5711	383	7	of	of	ADP
ejpam-5711	383	8	graph	graph	NOUN
ejpam-5711	383	9	.	.	PUNCT
ejpam-5711	384	1	southeast	southeast	ADJ
ejpam-5711	384	2	asian	asian	ADJ
ejpam-5711	384	3	bulletin	bulletin	NOUN
ejpam-5711	384	4	of	of	ADP
ejpam-5711	384	5	mathematics	mathematic	NOUN
ejpam-5711	384	6	,	,	PUNCT
ejpam-5711	384	7	40:59–80	40:59–80	PROPN
ejpam-5711	384	8	,	,	PUNCT
ejpam-5711	384	9	2016	2016	NUM
ejpam-5711	384	10	.	.	PUNCT
ejpam-5711	385	1	[	[	X
ejpam-5711	385	2	10	10	NUM
ejpam-5711	385	3	]	]	X
ejpam-5711	385	4	i.	i.	PROPN
ejpam-5711	385	5	gutman	gutman	PROPN
ejpam-5711	385	6	.	.	PUNCT
ejpam-5711	386	1	the	the	DET
ejpam-5711	386	2	acyclic	acyclic	ADJ
ejpam-5711	386	3	polynomial	polynomial	NOUN
ejpam-5711	386	4	of	of	ADP
ejpam-5711	386	5	a	a	DET
ejpam-5711	386	6	graph	graph	NOUN
ejpam-5711	386	7	.	.	PUNCT
ejpam-5711	387	1	publications	publication	NOUN
ejpam-5711	387	2	de	de	X
ejpam-5711	387	3	l’institut	l’institut	X
ejpam-5711	387	4	mathématique	mathématique	PROPN
ejpam-5711	387	5	,	,	PUNCT
ejpam-5711	387	6	22(36):63–69	22(36):63–69	NUM
ejpam-5711	387	7	,	,	PUNCT
ejpam-5711	387	8	1997	1997	NUM
ejpam-5711	387	9	.	.	PUNCT
ejpam-5711	388	1	[	[	X
ejpam-5711	388	2	11	11	NUM
ejpam-5711	388	3	]	]	SYM
ejpam-5711	388	4	i.	i.	PROPN
ejpam-5711	388	5	gutman	gutman	PROPN
ejpam-5711	388	6	and	and	CCONJ
ejpam-5711	388	7	n.	n.	PROPN
ejpam-5711	388	8	trinajstic	trinajstic	PROPN
ejpam-5711	388	9	.	.	PUNCT
ejpam-5711	389	1	graph	graph	NOUN
ejpam-5711	389	2	theory	theory	NOUN
ejpam-5711	389	3	and	and	CCONJ
ejpam-5711	389	4	molecular	molecular	ADJ
ejpam-5711	389	5	orbital	orbital	NOUN
ejpam-5711	389	6	.	.	PUNCT
ejpam-5711	390	1	total	total	ADJ
ejpam-5711	390	2	ϕ-electron	ϕ-electron	PROPN
ejpam-5711	390	3	energy	energy	NOUN
ejpam-5711	390	4	of	of	ADP
ejpam-5711	390	5	alternate	alternate	ADJ
ejpam-5711	390	6	hydrocarbons	hydrocarbon	NOUN
ejpam-5711	390	7	.	.	PUNCT
ejpam-5711	391	1	chemical	chemical	PROPN
ejpam-5711	391	2	physics	physics	PROPN
ejpam-5711	391	3	letters	letter	NOUN
ejpam-5711	391	4	,	,	PUNCT
ejpam-5711	391	5	17:535–538	17:535–538	NUM
ejpam-5711	391	6	,	,	PUNCT
ejpam-5711	391	7	1972	1972	NUM
ejpam-5711	391	8	.	.	PUNCT
ejpam-5711	392	1	[	[	X
ejpam-5711	392	2	12	12	NUM
ejpam-5711	392	3	]	]	PUNCT
ejpam-5711	392	4	h.	h.	PROPN
ejpam-5711	392	5	hosoya	hosoya	PROPN
ejpam-5711	392	6	.	.	PUNCT
ejpam-5711	393	1	on	on	ADP
ejpam-5711	393	2	some	some	DET
ejpam-5711	393	3	counting	counting	NOUN
ejpam-5711	393	4	polynomials	polynomial	NOUN
ejpam-5711	393	5	in	in	ADP
ejpam-5711	393	6	chemistry	chemistry	NOUN
ejpam-5711	393	7	.	.	PUNCT
ejpam-5711	394	1	discrete	discrete	ADJ
ejpam-5711	394	2	appl	appl	PROPN
ejpam-5711	394	3	.	.	PUNCT
ejpam-5711	394	4	math	math	PROPN
ejpam-5711	394	5	.	.	PUNCT
ejpam-5711	394	6	,	,	PUNCT
ejpam-5711	394	7	19:239	19:239	NUM
ejpam-5711	394	8	–	–	PUNCT
ejpam-5711	394	9	257	257	NUM
ejpam-5711	394	10	,	,	PUNCT
ejpam-5711	394	11	1988	1988	NUM
ejpam-5711	394	12	.	.	PUNCT
ejpam-5711	395	1	[	[	X
ejpam-5711	395	2	13	13	NUM
ejpam-5711	395	3	]	]	X
ejpam-5711	395	4	y.	y.	PROPN
ejpam-5711	395	5	c.	c.	PROPN
ejpam-5711	395	6	kwun	kwun	PROPN
ejpam-5711	395	7	,	,	PUNCT
ejpam-5711	395	8	a.	a.	PROPN
ejpam-5711	395	9	ali	ali	PROPN
ejpam-5711	395	10	,	,	PUNCT
ejpam-5711	395	11	w.	w.	PROPN
ejpam-5711	395	12	nazeer	nazeer	PROPN
ejpam-5711	395	13	,	,	PUNCT
ejpam-5711	395	14	m.	m.	PROPN
ejpam-5711	395	15	a.	a.	PROPN
ejpam-5711	395	16	chaudhary	chaudhary	PROPN
ejpam-5711	395	17	,	,	PUNCT
ejpam-5711	395	18	and	and	CCONJ
ejpam-5711	395	19	s.	s.	PROPN
ejpam-5711	395	20	m.	m.	PROPN
ejpam-5711	395	21	kang	kang	PROPN
ejpam-5711	395	22	.	.	PUNCT
ejpam-5711	396	1	m	m	PROPN
ejpam-5711	396	2	-	-	ADJ
ejpam-5711	396	3	polynomial	polynomial	ADJ
ejpam-5711	396	4	and	and	CCONJ
ejpam-5711	396	5	degree	degree	NOUN
ejpam-5711	396	6	-	-	PUNCT
ejpam-5711	396	7	based	base	VERB
ejpam-5711	396	8	topological	topological	ADJ
ejpam-5711	396	9	indices	index	NOUN
ejpam-5711	396	10	of	of	ADP
ejpam-5711	396	11	triangular	triangular	NOUN
ejpam-5711	396	12	,	,	PUNCT
ejpam-5711	396	13	hourglass	hourglass	NOUN
ejpam-5711	396	14	and	and	CCONJ
ejpam-5711	396	15	jagged	jagged	ADJ
ejpam-5711	396	16	-	-	PUNCT
ejpam-5711	396	17	rectangle	rectangle	NOUN
ejpam-5711	396	18	benzenoid	benzenoid	NOUN
ejpam-5711	396	19	systems	system	NOUN
ejpam-5711	396	20	.	.	PUNCT
ejpam-5711	397	1	journal	journal	NOUN
ejpam-5711	397	2	of	of	ADP
ejpam-5711	397	3	chemistry	chemistry	NOUN
ejpam-5711	397	4	,	,	PUNCT
ejpam-5711	397	5	page	page	NOUN
ejpam-5711	397	6	8	8	NUM
ejpam-5711	397	7	pages	page	NOUN
ejpam-5711	397	8	,	,	PUNCT
ejpam-5711	397	9	2018	2018	NUM
ejpam-5711	397	10	.	.	PUNCT
ejpam-5711	398	1	[	[	X
ejpam-5711	398	2	14	14	NUM
ejpam-5711	398	3	]	]	X
ejpam-5711	398	4	c.	c.	PROPN
ejpam-5711	398	5	p.	p.	PROPN
ejpam-5711	398	6	li	li	PROPN
ejpam-5711	398	7	,	,	PUNCT
ejpam-5711	398	8	c.	c.	PROPN
ejpam-5711	398	9	zhonglin	zhonglin	PROPN
ejpam-5711	398	10	,	,	PUNCT
ejpam-5711	398	11	m.	m.	PROPN
ejpam-5711	398	12	munir	munir	PROPN
ejpam-5711	398	13	,	,	PUNCT
ejpam-5711	398	14	k.	k.	PROPN
ejpam-5711	398	15	yasmin	yasmin	PROPN
ejpam-5711	398	16	,	,	PUNCT
ejpam-5711	398	17	and	and	CCONJ
ejpam-5711	398	18	j.	j.	PROPN
ejpam-5711	398	19	b.	b.	PROPN
ejpam-5711	398	20	liu	liu	PROPN
ejpam-5711	398	21	.	.	PUNCT
ejpam-5711	399	1	m	m	PROPN
ejpam-5711	399	2	-	-	ADJ
ejpam-5711	399	3	polynomial	polynomial	ADJ
ejpam-5711	399	4	and	and	CCONJ
ejpam-5711	399	5	topological	topological	ADJ
ejpam-5711	399	6	indices	index	NOUN
ejpam-5711	399	7	of	of	ADP
ejpam-5711	399	8	linear	linear	ADJ
ejpam-5711	399	9	chains	chain	NOUN
ejpam-5711	399	10	of	of	ADP
ejpam-5711	399	11	benzene	benzene	NOUN
ejpam-5711	399	12	,	,	PUNCT
ejpam-5711	399	13	napthalene	napthalene	NOUN
ejpam-5711	399	14	and	and	CCONJ
ejpam-5711	399	15	anthracene	anthracene	NOUN
ejpam-5711	399	16	.	.	PUNCT
ejpam-5711	400	1	mathematical	mathematical	ADJ
ejpam-5711	400	2	biosciences	bioscience	NOUN
ejpam-5711	400	3	and	and	CCONJ
ejpam-5711	400	4	engineering	engineering	NOUN
ejpam-5711	400	5	,	,	PUNCT
ejpam-5711	400	6	17(3):2384–2398	17(3):2384–2398	NUM
ejpam-5711	400	7	,	,	PUNCT
ejpam-5711	400	8	2020	2020	NUM
ejpam-5711	400	9	.	.	PUNCT
ejpam-5711	401	1	[	[	X
ejpam-5711	401	2	15	15	NUM
ejpam-5711	401	3	]	]	X
ejpam-5711	401	4	j.	j.	PROPN
ejpam-5711	401	5	b.	b.	PROPN
ejpam-5711	401	6	liu	liu	PROPN
ejpam-5711	401	7	,	,	PUNCT
ejpam-5711	401	8	w.	w.	PROPN
ejpam-5711	401	9	gao	gao	PROPN
ejpam-5711	401	10	,	,	PUNCT
ejpam-5711	401	11	m.	m.	PROPN
ejpam-5711	401	12	k.	k.	PROPN
ejpam-5711	401	13	siddiqui	siddiqui	PROPN
ejpam-5711	401	14	,	,	PUNCT
ejpam-5711	401	15	and	and	CCONJ
ejpam-5711	401	16	m.	m.	PROPN
ejpam-5711	401	17	r.	r.	PROPN
ejpam-5711	401	18	farhani	farhani	PROPN
ejpam-5711	401	19	.	.	PUNCT
ejpam-5711	402	1	computing	compute	VERB
ejpam-5711	402	2	three	three	NUM
ejpam-5711	402	3	topological	topological	ADJ
ejpam-5711	402	4	indices	index	NOUN
ejpam-5711	402	5	for	for	ADP
ejpam-5711	402	6	titania	titania	NOUN
ejpam-5711	402	7	nanotubes	nanotube	NOUN
ejpam-5711	402	8	tio2	tio2	NOUN
ejpam-5711	402	9	[	[	X
ejpam-5711	402	10	m	m	X
ejpam-5711	402	11	,	,	PUNCT
ejpam-5711	402	12	n	n	CCONJ
ejpam-5711	402	13	]	]	PUNCT
ejpam-5711	402	14	.	.	PUNCT
ejpam-5711	403	1	akce	akce	PROPN
ejpam-5711	403	2	international	international	PROPN
ejpam-5711	403	3	journal	journal	NOUN
ejpam-5711	403	4	of	of	ADP
ejpam-5711	403	5	graphs	graph	NOUN
ejpam-5711	403	6	and	and	CCONJ
ejpam-5711	403	7	combinator	combinator	NOUN
ejpam-5711	403	8	,	,	PUNCT
ejpam-5711	403	9	13(3):255–260	13(3):255–260	NUM
ejpam-5711	403	10	,	,	PUNCT
ejpam-5711	403	11	2016	2016	NUM
ejpam-5711	403	12	.	.	PUNCT
ejpam-5711	404	1	[	[	X
ejpam-5711	404	2	16	16	NUM
ejpam-5711	404	3	]	]	X
ejpam-5711	404	4	b.	b.	PROPN
ejpam-5711	404	5	b.	b.	PROPN
ejpam-5711	404	6	mandelbrot	mandelbrot	PROPN
ejpam-5711	404	7	.	.	PUNCT
ejpam-5711	405	1	the	the	DET
ejpam-5711	405	2	fractal	fractal	ADJ
ejpam-5711	405	3	geometry	geometry	NOUN
ejpam-5711	405	4	of	of	ADP
ejpam-5711	405	5	nature	nature	NOUN
ejpam-5711	405	6	.	.	PUNCT
ejpam-5711	406	1	times	time	NOUN
ejpam-5711	406	2	books	book	NOUN
ejpam-5711	406	3	,	,	PUNCT
ejpam-5711	406	4	1982	1982	NUM
ejpam-5711	406	5	.	.	PUNCT
ejpam-5711	407	1	[	[	X
ejpam-5711	407	2	17	17	NUM
ejpam-5711	407	3	]	]	PUNCT
ejpam-5711	407	4	m.	m.	NOUN
ejpam-5711	407	5	munir	munir	PROPN
ejpam-5711	407	6	,	,	PUNCT
ejpam-5711	407	7	w.	w.	PROPN
ejpam-5711	407	8	nazeer	nazeer	PROPN
ejpam-5711	407	9	,	,	PUNCT
ejpam-5711	407	10	s.	s.	PROPN
ejpam-5711	407	11	rafique	rafique	PROPN
ejpam-5711	407	12	,	,	PUNCT
ejpam-5711	407	13	and	and	CCONJ
ejpam-5711	407	14	s.	s.	PROPN
ejpam-5711	407	15	m.	m.	PROPN
ejpam-5711	407	16	kang	kang	PROPN
ejpam-5711	407	17	.	.	PUNCT
ejpam-5711	408	1	m	m	PROPN
ejpam-5711	408	2	-	-	ADJ
ejpam-5711	408	3	polynomial	polynomial	ADJ
ejpam-5711	408	4	and	and	CCONJ
ejpam-5711	408	5	degree	degree	NOUN
ejpam-5711	408	6	-	-	PUNCT
ejpam-5711	408	7	based	base	VERB
ejpam-5711	408	8	topological	topological	ADJ
ejpam-5711	408	9	indices	index	NOUN
ejpam-5711	408	10	of	of	ADP
ejpam-5711	408	11	polyhex	polyhex	NOUN
ejpam-5711	408	12	nanotubes	nanotube	NOUN
ejpam-5711	408	13	.	.	PUNCT
ejpam-5711	409	1	symmetry	symmetry	NOUN
ejpam-5711	409	2	,	,	PUNCT
ejpam-5711	409	3	8(12):149	8(12):149	PROPN
ejpam-5711	409	4	,	,	PUNCT
ejpam-5711	409	5	2016	2016	NUM
ejpam-5711	409	6	.	.	PUNCT
ejpam-5711	410	1	[	[	X
ejpam-5711	410	2	18	18	NUM
ejpam-5711	410	3	]	]	PUNCT
ejpam-5711	410	4	m.	m.	NOUN
ejpam-5711	410	5	munir	munir	PROPN
ejpam-5711	410	6	,	,	PUNCT
ejpam-5711	410	7	w.	w.	PROPN
ejpam-5711	410	8	nazeer	nazeer	PROPN
ejpam-5711	410	9	,	,	PUNCT
ejpam-5711	410	10	s.	s.	PROPN
ejpam-5711	410	11	rafique	rafique	PROPN
ejpam-5711	410	12	,	,	PUNCT
ejpam-5711	410	13	and	and	CCONJ
ejpam-5711	410	14	s.	s.	PROPN
ejpam-5711	410	15	m.	m.	PROPN
ejpam-5711	410	16	kang	kang	PROPN
ejpam-5711	410	17	.	.	PUNCT
ejpam-5711	411	1	m	m	PROPN
ejpam-5711	411	2	-	-	ADJ
ejpam-5711	411	3	polynomial	polynomial	ADJ
ejpam-5711	411	4	and	and	CCONJ
ejpam-5711	411	5	related	relate	VERB
ejpam-5711	411	6	topological	topological	ADJ
ejpam-5711	411	7	indices	index	NOUN
ejpam-5711	411	8	of	of	ADP
ejpam-5711	411	9	nanostar	nanostar	ADJ
ejpam-5711	411	10	dendrimers	dendrimer	NOUN
ejpam-5711	411	11	.	.	PUNCT
ejpam-5711	412	1	symmetry	symmetry	PROPN
ejpam-5711	412	2	,	,	PUNCT
ejpam-5711	412	3	8(9):97	8(9):97	NUM
ejpam-5711	412	4	,	,	PUNCT
ejpam-5711	412	5	2016	2016	NUM
ejpam-5711	412	6	.	.	PUNCT
ejpam-5711	413	1	n.	n.	PROPN
ejpam-5711	413	2	t.	t.	PROPN
ejpam-5711	413	3	sarhan	sarhan	PROPN
ejpam-5711	413	4	,	,	PUNCT
ejpam-5711	413	5	d.	d.	PROPN
ejpam-5711	413	6	a.	a.	PROPN
ejpam-5711	413	7	ali	ali	PROPN
ejpam-5711	413	8	,	,	PUNCT
ejpam-5711	413	9	g.	g.	PROPN
ejpam-5711	413	10	h.	h.	PROPN
ejpam-5711	414	1	mohiaddin	mohiaddin	PROPN
ejpam-5711	414	2	/	/	SYM
ejpam-5711	414	3	eur	eur	PROPN
ejpam-5711	414	4	.	.	PUNCT
ejpam-5711	415	1	j.	j.	PROPN
ejpam-5711	415	2	pure	pure	PROPN
ejpam-5711	415	3	appl	appl	PROPN
ejpam-5711	415	4	.	.	PROPN
ejpam-5711	415	5	math	math	PROPN
ejpam-5711	415	6	,	,	PUNCT
ejpam-5711	415	7	18	18	NUM
ejpam-5711	415	8	(	(	PUNCT
ejpam-5711	415	9	1	1	NUM
ejpam-5711	415	10	)	)	PUNCT
ejpam-5711	415	11	(	(	PUNCT
ejpam-5711	415	12	2025	2025	NUM
ejpam-5711	415	13	)	)	PUNCT
ejpam-5711	415	14	,	,	PUNCT
ejpam-5711	415	15	5711	5711	NUM
ejpam-5711	415	16	15	15	NUM
ejpam-5711	415	17	of	of	ADP
ejpam-5711	415	18	15	15	NUM
ejpam-5711	415	19	[	[	SYM
ejpam-5711	415	20	19	19	NUM
ejpam-5711	415	21	]	]	PUNCT
ejpam-5711	415	22	s.	s.	PROPN
ejpam-5711	415	23	nikolic	nikolic	PROPN
ejpam-5711	415	24	,	,	PUNCT
ejpam-5711	415	25	g.	g.	PROPN
ejpam-5711	415	26	kovacevic	kovacevic	PROPN
ejpam-5711	415	27	,	,	PUNCT
ejpam-5711	415	28	a.	a.	NOUN
ejpam-5711	415	29	milicevic	milicevic	ADJ
ejpam-5711	415	30	,	,	PUNCT
ejpam-5711	415	31	and	and	CCONJ
ejpam-5711	415	32	n.	n.	PROPN
ejpam-5711	415	33	trinajstic	trinajstic	PROPN
ejpam-5711	415	34	.	.	PUNCT
ejpam-5711	416	1	the	the	DET
ejpam-5711	416	2	zagrab	zagrab	NOUN
ejpam-5711	416	3	indices	indice	VERB
ejpam-5711	416	4	30	30	NUM
ejpam-5711	416	5	years	year	NOUN
ejpam-5711	416	6	after	after	ADV
ejpam-5711	416	7	.	.	PUNCT
ejpam-5711	417	1	croa	croa	NOUN
ejpam-5711	417	2	.	.	PUNCT
ejpam-5711	418	1	chem	chem	PROPN
ejpam-5711	418	2	.	.	PUNCT
ejpam-5711	419	1	acta	acta	PROPN
ejpam-5711	419	2	,	,	PUNCT
ejpam-5711	419	3	76(2):113–124	76(2):113–124	PROPN
ejpam-5711	419	4	,	,	PUNCT
ejpam-5711	419	5	2003	2003	NUM
ejpam-5711	419	6	.	.	PUNCT
ejpam-5711	420	1	[	[	X
ejpam-5711	420	2	20	20	NUM
ejpam-5711	420	3	]	]	PUNCT
ejpam-5711	420	4	m.	m.	NOUN
ejpam-5711	420	5	randić.	randić.	PROPN
ejpam-5711	420	6	on	on	ADP
ejpam-5711	420	7	characterization	characterization	NOUN
ejpam-5711	420	8	of	of	ADP
ejpam-5711	420	9	molecular	molecular	ADJ
ejpam-5711	420	10	branching	branching	NOUN
ejpam-5711	420	11	.	.	PUNCT
ejpam-5711	421	1	journal	journal	NOUN
ejpam-5711	421	2	of	of	ADP
ejpam-5711	421	3	the	the	DET
ejpam-5711	421	4	american	american	PROPN
ejpam-5711	421	5	chemical	chemical	PROPN
ejpam-5711	421	6	society	society	PROPN
ejpam-5711	421	7	,	,	PUNCT
ejpam-5711	421	8	97:6609–6615	97:6609–6615	NUM
ejpam-5711	421	9	,	,	PUNCT
ejpam-5711	421	10	1975	1975	NUM
ejpam-5711	421	11	.	.	PUNCT
ejpam-5711	422	1	[	[	X
ejpam-5711	422	2	21	21	NUM
ejpam-5711	422	3	]	]	X
ejpam-5711	422	4	d.	d.	NOUN
ejpam-5711	422	5	vukicevic	vukicevic	PROPN
ejpam-5711	422	6	and	and	CCONJ
ejpam-5711	422	7	a.	a.	NOUN
ejpam-5711	422	8	graovac	graovac	PROPN
ejpam-5711	422	9	.	.	PUNCT
ejpam-5711	423	1	valence	valence	NOUN
ejpam-5711	423	2	connectivity	connectivity	NOUN
ejpam-5711	423	3	versus	versus	ADP
ejpam-5711	423	4	randic	randic	ADJ
ejpam-5711	423	5	,	,	PUNCT
ejpam-5711	423	6	zagrab	zagrab	NOUN
ejpam-5711	423	7	and	and	CCONJ
ejpam-5711	423	8	modified	modify	VERB
ejpam-5711	423	9	zagrab	zagrab	NOUN
ejpam-5711	423	10	index	index	NOUN
ejpam-5711	423	11	:	:	PUNCT
ejpam-5711	423	12	a	a	DET
ejpam-5711	423	13	linear	linear	ADJ
ejpam-5711	423	14	algorithm	algorithm	NOUN
ejpam-5711	423	15	to	to	PART
ejpam-5711	423	16	check	check	VERB
ejpam-5711	423	17	discriminative	discriminative	NOUN
ejpam-5711	423	18	properties	property	NOUN
ejpam-5711	423	19	of	of	ADP
ejpam-5711	423	20	indices	index	NOUN
ejpam-5711	423	21	in	in	ADP
ejpam-5711	423	22	acyclic	acyclic	ADJ
ejpam-5711	423	23	molecular	molecular	ADJ
ejpam-5711	423	24	graphs	graph	NOUN
ejpam-5711	423	25	.	.	PUNCT
ejpam-5711	424	1	croatica	croatica	PROPN
ejpam-5711	424	2	chemica	chemica	PROPN
ejpam-5711	424	3	acta	acta	PROPN
ejpam-5711	424	4	,	,	PUNCT
ejpam-5711	424	5	77(3):501–508	77(3):501–508	NUM
ejpam-5711	424	6	,	,	PUNCT
ejpam-5711	424	7	2004	2004	NUM
ejpam-5711	424	8	.	.	PUNCT
ejpam-5711	425	1	[	[	X
ejpam-5711	425	2	22	22	NUM
ejpam-5711	425	3	]	]	PUNCT
ejpam-5711	425	4	h.	h.	PROPN
ejpam-5711	425	5	wiener	wiener	PROPN
ejpam-5711	425	6	.	.	PUNCT
ejpam-5711	426	1	structural	structural	ADJ
ejpam-5711	426	2	determination	determination	NOUN
ejpam-5711	426	3	of	of	ADP
ejpam-5711	426	4	paraffin	paraffin	NOUN
ejpam-5711	426	5	boiling	boiling	NOUN
ejpam-5711	426	6	points	point	NOUN
ejpam-5711	426	7	.	.	PUNCT
ejpam-5711	427	1	journal	journal	NOUN
ejpam-5711	427	2	of	of	ADP
ejpam-5711	427	3	the	the	DET
ejpam-5711	427	4	american	american	PROPN
ejpam-5711	427	5	chemical	chemical	PROPN
ejpam-5711	427	6	society	society	PROPN
ejpam-5711	427	7	,	,	PUNCT
ejpam-5711	427	8	69:17–20	69:17–20	NUM
ejpam-5711	427	9	,	,	PUNCT
ejpam-5711	427	10	1947	1947	NUM
ejpam-5711	427	11	.	.	PUNCT